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Exploring dynamics of plant–herbivore interactions: bifurcation analysis and chaos control with Holling type-II functional response

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Abstract

In this study, we examine the plant–herbivore discrete model of apple twig borer and grape vine interaction, with a particular emphasis on the extended weak-predator response to Holling type-II response. We explore the dynamical and qualitative analysis of this model and investigate the conditions for stability and bifurcation. Our study demonstrates the presence of the Neimark–Sacker bifurcation at the interior equilibrium and the transcritical bifurcation at the trivial equilibrium, both of which have biological feasibility. To avoid unpredictable outcomes due to bifurcation, we employ chaos control methods. Furthermore, to support our theoretical and mathematical findings, we develop numerical simulation techniques with examples. In summary, our research enhances the comprehension of the dynamics pertaining to interactions between plants and herbivores in the context of discrete-time population models.

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Authors and Affiliations

  1. Department of Mathematics, University of Poonch, Rawalakot, 12350, Pakistan

    Muhammad Sajjad Shabbir & Qamar Din

  2. Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, Campus of Leioa (Bizkaia), University of the Basque Country, 48940, Leioa, Spain

    Manuel De la Sen

  3. Centro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp-IICBA)/UAEM, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001 Col. Chamilpa, C.P. 62209, Cuernavaca, Morelos, México

    J. F. Gómez-Aguilar

Authors
  1. Muhammad Sajjad Shabbir
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  2. Qamar Din
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  3. Manuel De la Sen
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  4. J. F. Gómez-Aguilar
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Correspondence to Muhammad Sajjad Shabbir.

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Shabbir, M.S., Din, Q., De la Sen, M. et al. Exploring dynamics of plant–herbivore interactions: bifurcation analysis and chaos control with Holling type-II functional response. J. Math. Biol. 88, 8 (2024). https://doi.org/10.1007/s00285-023-02020-5

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  • DOI: https://doi.org/10.1007/s00285-023-02020-5

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