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Disorder-Induced Dynamics in Complex Networks Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-18 Antonio Palacios, Visarath In, Mani Amani
Disorder in parameters appears to influence the collective behavior of complex adaptive networks in ways that might seem unconventional. For instance, heterogeneities may, unexpectedly, lead to enhanced regions of existence of stable synchronization states. This behavior is unexpected because synchronization appears, generically, in symmetric networks with homogeneous components. Related works have
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Characterization of the Riccati and Abel Polynomial Differential Systems Having Invariant Algebraic Curves Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-10 Jaume Giné, Jaume Llibre
The Riccati polynomial differential systems are differential systems of the form x′=c0(x), y′=b0(x)+b1(x)y+b2(x)y2, where c0 and bi for i=0,1,2 are polynomial functions. We characterize all the Riccati polynomial differential systems having an invariant algebraic curve. We show that the coefficients of the first four highest degree terms of the polynomial in the variable y defining the invariant algebraic
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Periodic Orbit Dividing Surfaces in a Quartic Hamiltonian System with Three Degrees of Freedom – I Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Francisco Gonzalez Montoya, Matthaios Katsanikas, Stephen Wiggins
In prior work [Katsanikas & Wiggins, 2021a, 2021b, 2023c, 2023d], we introduced two methodologies for constructing Periodic Orbit Dividing Surfaces (PODS) tailored for Hamiltonian systems possessing three or more degrees of freedom. The initial approach, outlined in [Katsanikas & Wiggins, 2021a, 2023c], was applied to a quadratic Hamiltonian system in normal form having three degrees of freedom. Within
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Emergence Behavior Versus Physical-Like Behavior Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Xiaobo Hou, Wanshan Lin, Xueting Tian, Xutong Zhao
In this paper, we study the dynamical complexity of points with emergence behavior but without weak face behavior, especially for points without physical-like behavior in certain dynamical systems such as transitive Anosov systems. We use the tools of saturated sets to prove that these points show strong dynamical complexity in the sense of entropy, density and distributional chaos. We obtain some
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Spatiotemporal Dynamics of a General Two-Species System with Taxis Term Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Wenjie Zuo, Yongli Song
In this paper, we investigate the spatiotemporal dynamics in a diffusive two-species system with taxis term and general functional response, which means the directional movement of one species upward or downward the other one. The stability of positive equilibrium and the existences of Turing bifurcation, Turing–Hopf bifurcation and Turing–Turing bifurcation are investigated. An algorithm for calculating
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Controlled Quasi-Latitudinal Solutions for Ultra-Fast Spin-Torque Magnetization Switching Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Alessandro Fortunati, Massimiliano d’Aquino, Claudio Serpico
The aim of this paper is to present a novel class of time-dependent controls to realize ultra-fast magnetization switching in nanomagnets driven by spin-torques produced by spin-polarized electric currents. Magnetization dynamics in such complex systems is governed by the Landau–Lifshitz–Slonczewski equation which describes the precessional motion of (dimensionless) magnetization vector on the unit-sphere
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Multiobjective Optimization of Chaotic Image Encryption Based on ABC Algorithm and DNA Coding Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Jinwei Yu, Wei Xie, Langwen Zhang
As digital communication and storage continue to expand, the protection of image privacy information becomes increasingly critical. To safeguard sensitive visual information from unauthorized access, this paper proposes a novel image encryption scheme that integrates multiobjective Artificial Bee Colony (ABC) optimization algorithm and DNA coding. Multiple evaluation metrics including correlation relationship
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Exploring Iterated Implicit Function Systems: Existence and Properties of Attractors Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Zhong Dai, Shutang Liu
This paper investigates a type of iterated implicit function systems composed of equations Fn(x,y)=c, where Fn(x,y) is a continuous function, and c is a constant. The existence of attractors of iterated implicit function systems is proved based on different equation conditions, including the equation Fn(x,y)=c containing the implicit function or being αn-contractive about y. Meanwhile, we give definitions
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Stability and Bifurcation Analysis of a Spatially Size–Stage-Structured Model with Resting Phase Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Yajing Li, Zhihua Liu
In this paper, we consider a spatially size–stage-structured population dynamics model with resting phase. The primary objective of this model is to study size structure, stage structure, resting phase and spatial location simultaneously in a single population system. At first, we reformulate the problem as an abstract nondensely defined Cauchy problem. Then, taking advantage of the integrated semigroup
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Spatiotemporal and Trade-Off Dynamics in Prey–Predator Model with Domed Functional Response and Fear Effect Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Masoom Bhargava, Anshu, Balram Dubey
In the ecological scenario, predators often risk their lives pursuing dangerous prey, potentially reducing their chances of survival due to injuries. Prey, on the other hand, try to strike a balance between reproduction rates and safety. In our study, we introduce a two-dimensional prey–predator model inspired by Tostowaryk’s work, specifically focusing on the domed-shaped functional response observed
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Spatial Dynamics of a Competitive and Cooperative Model with Multiple Delay Effects: Turing Patterns and Hopf Bifurcation Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Yu Mu, Wing-Cheong Lo
Competing populations within an ecosystem often release chemicals during the interactions and diffusion processes. These chemicals can have diverse effects on competitors, ranging from inhibition to stimulation of species’ growth. This work constructs a competition model that incorporates stimulatory substances, spatial effects, and multiple time lags to investigate the combined impact of these phenomena
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Computation of Normal Form and Unfolding of Codimension-3 Zero-Hopf–Hopf Bifurcation Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Xin Xu, Xiaofang Zhang, Qinsheng Bi
The computation of the normal form as well as its unfolding is a key step to understand the topological structure of a bifurcation. Though a lot of results have been obtained, it still remains unsolved for higher co-dimensional bifurcations. The main purpose of this paper is devoted to the computation of a codimension-3 zero-Hopf–Hopf bifurcation, at which a zero as well as two pairs of pure imaginary
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Bifurcations and Exact Solutions of Optical Soliton Models in Fifth-Order Weakly Nonlocal Nonlinear Media Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Rong Wu, Guanrong Chen, Jibin Li
For the optical soliton model in fifth-order weakly nonlocal nonlinear media, to find its exact explicit solutions, the corresponding traveling wave system is formulated as a planar dynamical system with a singular straight line. Then, by using techniques from dynamical systems and singular traveling wave theory developed by [Li & Chen, 2007] to analyze the planar system and find the corresponding
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An Integrated Reservoir Predictor Based on Spatiotemporal Information Transformation Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Na Yang, Renhao Hong, Pei Chen, Zhengrong liu
Multistep prediction of high-dimensional time series is an essential and challenging task. In this study, we propose an integrated reservoir predictor for making accurate and robust multistep-ahead forecasts based on short-term high-dimensional time series. Initially, a conjugated pair of Spatiotemporal Information (STI) equations is derived using Takens’ embedding theory to transform the spatial information
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Crossing Limit Cycles in Planar Piecewise Linear Systems Separated by a Nonregular Line with Node–Node Type Critical Points Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Liping Sun, Zhengdong Du
In this paper, we investigate the existence and number of crossing limit cycles in a class of planar piecewise linear systems with node–node type critical points defined in two zones separated by a nonregular line formed by two rays emanated from the origin (0,0), which are the positive x- and y-axes. We focus our attention on the existence of two-point crossing limit cycles, which intersect the switching
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Attractor Merging and Amplitude Control of Hyperchaos in a Self-Reproducing Memristive Map Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-09 Yongxin Li, Chunbiao Li, Qing Zhong, Tengfei Lei, Sicong Liu
Memristor-type feedback provides a unique passage for chaos produced with easy control. In this work, a novel memristive map with amplitude control and coexisting hyperchaotic attractors is designed, in which two nonbifurcation parameters are extracted for partial amplitude control crossing the origin and total amplitude control. Attractor splitting and attractor merging are captured, which lead to
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Designing a Fully Current-Controlled Memristors-Based Oscillator Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-04-03 Yan Liang, Shichang Wang, Zhenzhou Lu, Yiqing Li, Kangtai Wang
One of the promising applications of locally-active memristors (LAMs) is to construct oscillators for oscillatory neural networks. By using two current-controlled (CC) LAMs, a fully CC LAM-based oscillator is designed in this paper. The oscillator principle originates from the small-signal inductive and capacitive impedance characteristics of two different CC LAMs, and thus extra reactance element
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Influence of Two-Frequency Rotational Modulation on the Dynamics of the Rayleigh–Bénard Convection in Water-Based Nanoliquids with Either AA7072 or AA7075 Nanoparticles Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-28 C. Kanchana, P. G. Siddheshwar, D. Laroze
The effect of time-periodic two-frequency rotation modulation on Rayleigh–Bénard convection in water with either AA7072 or AA7075 nanoparticles is investigated. The single-phase description of the Khanafer–Vafai–Lightstone model is used for modeling the nanoliquids. An asymptotic expansion procedure is adopted in the case of the linear stability to obtain the correction (due to modulation) to the Rayleigh
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Impact of Predator-Driven Allee and Spatiotemporal Effect on a Simple Predator–Prey Model Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-28 Kaushik Kayal, Sudip Samanta, Sourav Rana, Sagar Karmakar, Joydev Chattopadhyay
In this research paper, we consider a Leslie–Gower Reaction–Diffusion (RD) model with a predator-driven Allee term in the prey population. We derive conditions for the existence of nontrivial solutions, uniform boundedness, local stability at co-existing equilibrium points, and Hopf bifurcation criteria from the temporal system. We identify sufficient conditions for Turing instability with no-flux
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Bifurcations for Homoclinic Networks in Two-Dimensional Polynomial Systems Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-26 Albert C. J. Luo
The bifurcation theory for homoclinic networks with singular and nonsingular equilibriums is a key to understand the global dynamics of nonlinear dynamical systems, which will help one determine the dynamical behaviors of physical and engineering nonlinear systems. In this paper, the appearing and switching bifurcations for homoclinic networks through equilibriums in planar polynomial dynamical systems
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Functional Shift-Induced Degenerate Transcritical Neimark–Sacker Bifurcation in a Discrete Hypercycle Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-20 Ernest Fontich, Antoni Guillamon, Júlia Perona, Josep Sardanyés
In this paper, we investigate the impact of functional shifts in a time-discrete cross-catalytic system. We use the hypercycle model considering that one of the species shifts from a cooperator to a degrader. At the bifurcation caused by this functional shift, an invariant curve collapses to a point P while, simultaneously, two fixed points collide with P in a transcritical bifurcation. Moreover, all
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Learning Topological Horseshoe via Deep Neural Networks Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-19 Xiao-Song Yang, Junfeng Cheng
Deep Neural Networks (DNNs) have been successfully applied to investigations of numerical dynamics of finite-dimensional nonlinear systems such as ODEs instead of finding numerical solutions to ODEs via the traditional Runge–Kutta method and its variants. To show the advantages of DNNs, in this paper, we demonstrate that the DNNs are more efficient in finding topological horseshoes in chaotic dynamical
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Analysis of Successive Doubly Nested Mixed-Mode Oscillations Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-19 Hidetaka Ito, Naohiko Inaba
In previous works [Inaba & Kousaka, 2020; Inaba & Tsubone, 2020; Inaba et al., 2023], significant bifurcation structures referred to as nested Mixed-Mode Oscillations (MMOs) were found to be present in forced Bonhoeffer–van der Pol (BVP) oscillators. It is well known that unnested Mixed-Mode Oscillation-Incrementing Bifurcations (MMOIBs) can generate [A0,B0×m] oscillations (i.e. A0 followed by B0 repeated
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Bifurcation Regulations Induced by Joint Noise in a Tri-Rhythmic Van Der Pol System Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-19 Jing Yuan, Lijuan Ning, Ze Li
Tri-rhythmical nature has attracted extensive attention from scholars in describing the dynamical behaviors of self-sustained systems. In this paper, we consider a tri-rhythmic van der Pol system and give a bifurcation analysis of a stochastic tri-rhythmic self-sustained system under joint noise perturbation. Based on an approximate approach, we give the stationary probability density function of amplitudes
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Two-Parameter Bifurcations and Hidden Attractors in a Class of 3D Linear Filippov Systems Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-19 Zhouchao Wei, Fanrui Wang
We take into consideration two different kinds of two-parameter bifurcations in a class of 3D linear Filippov systems, namely pseudo-Bautin bifurcation and boundary equilibrium bifurcations for two scenarios. The bifurcation conditions for generating rich dynamic behaviors are established. The main objective is to investigate the effects of two parameters interacting simultaneously on a variety of
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A Nonlinear Megastable System with Diamond-Shaped Oscillators Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-19 Atefeh Ahmadi, Sridevi Sriram, Ahmed M. Ali Ali, Karthikeyan Rajagopal, Nikhil Pal, Sajad Jafari
Benefiting from trigonometric and hyperbolic functions, a nonlinear megastable chaotic system is reported in this paper. Its nonlinear equations without linear terms make the system dynamics much more complex. Its coexisting attractors’ shape is diamond-like; thus, this system is said to have diamond-shaped oscillators. State space and time series plots show the existence of coexisting chaotic attractors
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Slow Invariant Manifolds of Memristor-Based Chaotic Circuits Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Jean-Marc Ginoux, Riccardo Meucci, Guanrong Chen, Leon O. Chua
This work presents an efficient approach for computing the slow invariant manifold of the fourth-order canonical memristor-based Chua circuits using the flow curvature method. First, the magnetic-flux and charge characteristic curve is generated from the classical circuit with a piecewise-linear function. Then, the characteristic curve is generated from the circuit with the piecewise-linear function
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3D Generating Surfaces in Hamiltonian Systems with Three Degrees of Freedom – I Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Matthaios Katsanikas, Stephen Wiggins
In our earlier research (see [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b, 2023c]), we developed two methods for creating dividing surfaces, either based on periodic orbits or two-dimensional generating surfaces. These methods were specifically designed for Hamiltonian systems with three or more degrees of freedom. Our prior work extended these dividing surfaces to more complex structures such
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3D Generating Surfaces in Hamiltonian Systems with Three Degrees of Freedom – II Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Matthaios Katsanikas, Stephen Wiggins
Our paper is a continuation of a previous work referenced as [Katsanikas & Wiggins, 2024b]. In this new paper, we present a second method for computing three-dimensional generating surfaces in Hamiltonian systems with three degrees of freedom. These 3D generating surfaces are distinct from the Normally Hyperbolic Invariant Manifold (NHIM) and have the unique property of producing dividing surfaces
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Dynamic Complexities in Competing Parasitoid Species on a Shared Host Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Lijiao Jia, Yunil Roh, Guangri Piao, Il Hyo Jung
In this study, we extend the two-dimensional host–parasitoid model to a one-host–two-parasitoid model, whose dynamic behaviors are more complex. As evidence, exploring the dynamic interaction between a host and its parasitoids provides significant insight into the biological control. Specifically, we demonstrate the existence of equilibrium points and explore their local stability properties, which
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Bistability and Bifurcations of Tumor Dynamics with Immune Escape and the Chimeric Antigen Receptor T-Cell Therapy Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Shaoli Wang, Tengfei Wang, Xiyan Bai, Shaoping Ji, Tianhai Tian
Tumor immune escape refers to the inability of the immune system to clear tumor cells, which is one of the major obstacles in designing effective treatment schemes for cancer diseases. Although clinical studies have led to promising treatment outcomes, it is imperative to design theoretical models to investigate the long-term treatment effects. In this paper, we develop a mathematical model to study
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Weak Sensitive Compactness for Linear Operators Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Quanquan Yao, Peiyong Zhu
Let (X,T) be a linear dynamical system, where X is a separable Banach space and T:X→X is a bounded linear operator. We show that if (X,T) is invertible, then (X,T) is weakly sensitive compact if and only if (X,T) is thickly weakly sensitive compact; and that there exists a system (X×Y,T×S) such that: (1) (X×Y,T×S) is cofinitely weakly sensitive compact; (2) (X,T) and (Y,S) are weakly sensitive compact;
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Emergence of Hidden Strange Nonchaotic Attractors in a Rational Memristive Map Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Premraj Durairaj, Sathiyadevi Kanagaraj, Zhigang Zheng, Anitha Karthikeyan, Karthikeyan Rajagopal
To exemplify the existence of hidden strange nonchaotic attractors (HSNAs) and transition mechanism, we consider a rational memristive map with additional force. We find that the four-torus bifurcates into the eight-torus through torus doubling as a function of the control parameter. Following that, the formation of strange nonchaotic attractors occurs when increasing the control parameter. As a result
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Dynamic Relationship Between Informal Sector and Unemployment: A Mathematical Model Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 A. K. Misra, Mamta Kumari
Shortage of formal jobs, lack of skills in workforce and increasing human population proliferate the informal sector. This sector provides an opportunity to unskilled workers to gain skills along with earnings. In this paper, a deterministic nonlinear mathematical model is developed to study the effects of informal skill learning and job generation on unemployment. For the formulated system, feasibility
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Impact of Fear and Group Defense on the Dynamics of a Predator–Prey System Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Soumitra Pal, Sarbari Karmakar, Saheb Pal, Nikhil Pal, A. K. Misra, Joydev Chattopadhyay
To reduce the chance of predation, many prey species adopt group defense mechanisms. While it is commonly believed that such defense mechanisms lead to positive feedback on prey density, a closer observation reveals that it may impact the growth rate of species. This is because individuals invest more time and effort in defense rather than reproductive activities. In this study, we delve into a predator–prey
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Bifurcation Analysis of a Discrete Amensalism Model Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Xinli Hu, Hanghang Li, Fengde Chen
By using model discretization of the piecewise constant argument method, a discrete amensalism model with nonselective harvesting and Allee effect is formulated. The dynamic analysis of the model is studied and the existence and stability of the equilibrium point are discussed. The fold bifurcation and flip bifurcation at the equilibrium point of the system are proved by using the bifurcation theory
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Bifurcation Analysis of a Predator–Prey Model with Alternative Prey and Prey Refuges Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Wenzhe Cui, Yulin Zhao
In this paper, we study the codimensions of Hopf bifurcation and Bogdanov–Takens bifurcation of a predator–prey model with alternative prey and prey refuges, which was proposed by Chen et al. [2023]. The results show that the predator–prey model can undergo a supercritical Hopf bifurcation or a Bogdanov–Takens bifurcation of codimension two under certain parameter conditions. It means that there are
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Coupled HR–HNN Neuron with a Locally Active Memristor Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Lili Huang, Shaotian Wang, Tengfei Lei, Keyu Huang, Chunbiao Li
Local activity could be the source for complexity. In this study, a multistable locally active memristor is proposed, whose nonvolatile memory, as well as locally active characteristics, is validated by the power-off plot and DC V–I plot. Based on the two-dimensional Hindmarsh–Rose neuron and a one-dimensional Hopfield neuron, a simple neural network is constructed by connecting the two neurons with
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Optimal and Poor Synchronizations of Directionally Coupled Phase-Coherent Chaotic Oscillators Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Yong Lei, Xin-Jian Xu, Xiaofan Wang
We study directionally coupled phase-coherent chaotic oscillators in complex networks. We introduce an adjusted Lyapunov function that incorporates the frequencies of the oscillators and the interaction structure. Using the well-known Rössler system as an example, we address two optimization problems: frequency allocation and network design. Through numerical experiments, we demonstrate that the systematic
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Stabilization of Laminars in Chaos Intermittency Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Michiru Katayama, Kenji Ikeda, Tetsushi Ueta
Chaos intermittency is composed of a laminar regime, which exhibits almost periodic motion, and a burst regime, which exhibits chaotic motion; it is known that in chaos intermittency, switching between these regimes occurs irregularly. In the laminar regime of chaos intermittency, the periodic solution before the saddle node bifurcation is closely related to its generation, and its behavior becomes
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Stability, Bifurcation and Dynamics in a Network with Delays Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Xu Xu, Jianming Liu
In real-world networks, due to complex topological structures and uncertainties such as time delays, uncontrolled systems may generate instability and complexity, thereby degrading network performance. This paper provides a detailed analysis of the stability, Hopf bifurcation, and complex dynamics of a networked system under delayed feedback control. Based on the linear stability method and Hopf bifurcation
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From 1D Endomorphism to Multidimensional Hénon Map: Persistence of Bifurcation Structure Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 V. N. Belykh, N. V. Barabash, D. A. Grechko
The renowned 2D invertible Hénon map turns into 1D noninvertible quadratic map when its leading parameter b becomes zero. This well-known link was studied by Mira who demonstrated that the bifurcation set of Hénon diffeomorphism is similar to his “box-within-a-box” bifurcation structure of 1D endomorphism. In general, such similarity has not been strictly established, especially in multidimensional
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Study of Short-Term and Long-Term Memories by Hodgkin–Huxley Memristor Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 L. Wen, C. K. Ong
Long-term memory (LTM ) and short-term memory (STM ) and their evolution from one to the other are important mechanisms to understand brain memory. We use the Hodgkin–Huxley (HH ) model, a well-tested and closest model to biological neurons and synapses, to shine some light on LTM and STM memorization mechanisms. The role of Na+ and K+ion channels playing in LTM and STM process is carefully examined
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On–Off Intermittency and Long-Term Reactivity in a Host–Parasitoid Model with a Deterministic Driver Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-12 Fasma Diele, Deborah Lacitignola, Angela Monti
Bursting behaviors, driven by environmental variability, can substantially influence ecosystem services and functions and have the potential to cause abrupt population breakouts in host–parasitoid systems. We explore the impact of environment on the host–parasitoid interaction by investigating separately the effect of grazing-dependent habitat variation on the host density and the effect of environmental
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Nonlinear Dynamic Analysis and Forecasting of Symmetric Aerostatic Cavities Bearing Systems Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-16 Ta-Jen Peng, Ping-Huan Kuo, Wei-Cheng Huang, Cheng-Chi Wang
Symmetric Aerostatic Cavities Bearing (SACB) systems have attracted increasing attention in the field of high-precision machinery, particularly rotational mechanisms applied at ultra-high speeds. In an air bearing system, the air bearing serves as the main support, and the load-carrying capacity is not as high as that of oil film bearings. However, the aero-spindle can operate at considerably high
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Multiparameter Bifurcation Analysis of Power Systems Integrating Large-Scale Solar Photovoltaic and Wind Farms Power Plants Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-15 Abdelaziz Salah Saidi, Muneer Parayangat, Mohamed Ali Rakrouki, Saad M. Saad, Naser El Naily
In this paper, we propose a novel codimension-three-parameter bifurcation analysis of equilibria and limit cycles when integrating Renewable Energy Sources (RESs) power plants with an exponential static load model. The study investigates the effect of solar photovoltaic generation margin, wind power generation margin, and loading factor on the local bifurcation of the modified IEEE nine-bus system
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Transition and Propagation of Epilepsy in an Improved Epileptor Model Coupled with Astrocyte Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-11 Kangning An, Lin Du, Honghui Zhang, Zhuan Shen, Xiaojuan Sun
In this paper, a tripartite synapse network is constructed to examine external and internal triggering factors of epilepsy transition and propagation in neurons with the Epileptor-2 model. We first explore the external stimuli in the environment that induce epileptic activities and transition behaviors among Ictal Discharges (IDs) and Interictal Discharges (IIDs) states. The higher the strength and
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Dynamic Analysis of a Ratio-Dependent Food Chain Model with Prey-Taxis Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-09 Zhuzhen Liao, Cui Song, Zhi-Cheng Wang
In this paper, we consider a food chain model with ratio-dependent functional response and prey-taxis. We first investigate the global existence and boundedness of the unique positive classical solutions of the system in a bounded domain with smooth boundary and Neumann boundary conditions. Then, we analyze the local stability of the system and the existence of Hopf bifurcation. In addition, we prove
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A Lightweight CNN Based on Memristive Stochastic Computing for Electronic Nose Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Bin Yang, Tao Chen, Ai Chen, Shukai Duan, Lidan Wang
Gas detection plays different roles in different environments. Traditional algorithms implemented on electronic nose for gas detection and recognition have high complexity and cannot resist device drift. In response to the above issues, we propose a convolutional neural network based on memristive Stochastic Computing (SC), which combines the characteristics of small devices and low power consumption
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Stability Analysis and Simulation of a Delayed Dengue Transmission Model with Logistic Growth and Nonlinear Incidence Rate Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Fangkai Guo, Xiaohong Tian
In this work, a dengue transmission model with logistic growth and time delay (τ) is investigated. Through detailed mathematical analysis, the local stability of a disease-free equilibrium and an endemic equilibrium is discussed, the existence of Hopf bifurcation and stability switch is established, and it is proved that the system is permanent if the basic reproduction number is greater than 1. On
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Four Limit Cycles of Three-Dimensional Discontinuous Piecewise Differential Systems Having a Sphere as Switching Manifold Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Louiza Baymout, Rebiha Benterki
Because of their applications, the study of piecewise-linear differential systems has become increasingly important in recent years. This type of system already exists to model many different natural phenomena in physics, biology, economics, etc. As is well known, the study of the qualitative theory of piecewise differential systems focuses mainly on limit cycles. Most papers studying the problem of
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Dynamics of a Class of Prey–Predator Models with Singular Perturbation and Distributed Delay Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Jie Gao, Yue Zhang
In this paper, two prey–predator models with distributed delays are presented based on the growth and loss rates of the predator, which are much smaller than that of the prey, leading to a singular perturbation problem. It is obtained that Hopf bifurcation can occur, where the coexistence equilibrium becomes unstable leading to a stable limit cycle. Subsequently, considering the perturbation parameter
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Global Phase Portraits of Piecewise Quadratic Differential Systems with a Pseudo-Center Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Meriem Barkat, Rebiha Benterki, Enrique Ponce
This paper deals with the global dynamics of planar piecewise smooth differential systems constituted by two different vector fields separated by one straight line that passes through the origin. From a quasi-canonical family of piecewise quadratic differential systems with a pseudo-focus point at the origin, which has six parameters, we investigate the subfamilies where the origin is indeed a pseudo-center
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Geometrical and Numerical Analysis of Predator–Prey System Based on the Allee Effect in Predator Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 M. K. Gupta, Abha Sahu, C. K. Yadav
This study explores the complex dynamics of the predator–prey interactions, with a specific emphasis on the influence of the Allee effect on the predator population. We examined the fundamental mathematical characteristics of the model under consideration, such as the positivity of the system and the boundedness of the solutions. We investigated the equilibrium points and analyzed their stability using
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Finite-Time Synchronization of Fractional-Order Nonlinear Systems with State-Dependent Delayed Impulse Control Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 P. Gokul, S. S. Mohanrasu, A. Kashkynbayev, R. Rakkiyappan
This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order
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Bifurcations of Sliding Heteroclinic Cycles in Three-Dimensional Filippov Systems Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Yousu Huang, Qigui Yang
Global bifurcations with sliding have rarely been studied in three-dimensional piecewise smooth systems. In this paper, codimension-2 bifurcations of nondegenerate sliding heteroclinic cycle Γ are investigated in three-dimensional Filippov systems. Two cases of sliding heteroclinic cycle are discussed: (C1) connecting two saddle-foci, (C2) connecting one saddle-focus and one saddle. It is proved that
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Existence and Uniqueness of a Canard Cycle with Cyclicity at Most Two in a Singularly Perturbed Leslie–Gower Predator–Prey Model with Prey Harvesting Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Zhenshu Wen, Tianyu Shi
Yao and Huzak [2022] proved that the cyclicity of canard cycles in a singularly perturbed Leslie–Gower predator–prey model with prey harvesting is at most two in a region of parameters. In this paper, we further show that there exists only one canard cycle with cyclicity at most two under explicit parameters conditions.
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The Effects of Negative Regulation on the Dynamical Transition in Epileptic Network Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Songan Hou, Haodong Wang, Denggui Fan, Ying Yu, Qingyun Wang
The transiting mechanism of abnormal brain functional activities, such as the epileptic seizures, has not been fully elucidated. In this study, we employ a probabilistic neural network model to investigate the impact of negative regulation, including negative connections and negative inputs, on the dynamical transition behavior of network dynamics. It is observed that negative connections significantly
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Bifurcations and Exact Solutions of a Cantilever Beam Vibration Model Without Damping and Forced Terms Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2024-03-06 Jinsen Zhuang, Guanrong Chen, Jibin Li
For the cantilever beam vibration model without damping and forced terms, the corresponding differential system is a planar dynamical system with some singular straight lines. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by [Li & Chen, 2007] to analyze its corresponding differential system, the bifurcations and the dynamical behaviors of
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Memory Maps with Elliptical Trajectories Int. J. Bifurcat. Chaos (IF 2.2) Pub Date : 2023-08-05 Ted Szylowiec, Paweł Góra
A family of maps with memory, parameterized by α, is shown to have either periodic trajectories or dense trajectories on ellipses which support absolutely continuous invariant measures. Furthermore, for 0<α<12, i.e. α=2cos𝜃2cos𝜃−1 with 𝜃=r(2π) and 14