As a circuit component with memory function, memristors have significant nonlinear physical characteristics and are widely used in the study of chaotic circuits and artificial neural networks. Given the superconducting quantum properties of Josephson junctions, various functional circuits and their applications, including memristors and Josephson junctions, have attracted widespread attention in recent years. This paper aims to study the nonlinear dynamic behavior, state switching characteristics, memory characteristics, and Hamiltonian energy calculation of a phototub chaotic circuit based on memristor and Josephson junction. Firstly, by utilizing the nonlinear physical characteristics of memristors and the superconducting quantum properties of Josephson junctions, a type of memristor coupled Josephson junction resonant circuit model is constructed by simultaneously introducing memristor and Josephson junction into the resonant circuit, selecting appropriate electronic components in a series parallel manner, and further exploring the memory mechanism and electromagnetic induction effect of memristor. Then, through dimensionless transformation, based on nonlinear dynamics and control theory and numerical simulation, the complex chaotic characteristics of its dynamic system are thoroughly studied. Lastly, in order to explore ways to reduce the energy storage of components in resonant coupled circuit systems with memristors, the Hamiltonian energy function of the coupled network containing memristor is calculated and analyzed. This study will play a certain expanding role in the nonlinear dynamic analysis and application of memristor functional circuits.

忆阻器作为一种具有记忆功能的电路元件，具有显着的非线性物理特性，广泛应用于混沌电路和人工神经网络的研究中。鉴于约瑟夫森结的超导量子特性，包括忆阻器和约瑟夫森结在内的各种功能电路及其应用近年来引起了广泛的关注。本文旨在研究基于忆阻器和约瑟夫森结的光电管混沌电路的非线性动态行为、状态切换特性、存储特性以及哈密顿能量计算。首先，利用忆阻器的非线性物理特性和约瑟夫森结的超导量子特性，通过在谐振电路中同时引入忆阻器和约瑟夫森结，选择串联合适的电子元件，构建了一种忆阻器耦合约瑟夫森结谐振电路模型。并联方式，进一步探索忆阻器的记忆机制和电磁感应效应。然后，通过无量纲变换，基于非线性动力学与控制理论和数值模拟，深入研究其动态系统的复杂混沌特性。最后，为了探索减少忆阻器谐振耦合电路系统中元件储能的方法，对包含忆阻器的耦合网络的哈密顿能量函数进行了计算和分析。本研究将对忆阻器功能电路的非线性动态分析和应用起到一定的拓展作用。