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<p>The objective of this study is to examine the dynamic behavior of a conformable fractional-order predator–prey system with a Holling-III type functional response. The fractional-order system is transformed into a discrete model through a discretization process. The fixed points are analyzed for both their existence and uniqueness. We then assess the local stability of the two fixed points using linearization techniques, and use the center manifold theorem and bifurcation theory to identify conditions for period-doubling and Neimark–Sacker bifurcations. To verify our findings, we perform numerical simulations and compute the maximum Lyapunov exponents to confirm the presence of chaotic behavior.</p>

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Qualitative behavior for a discretized conformable fractional-order predator–prey model

  • 期刊论文

  • 发表日期：

    2025年2月16日

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  • Messaoud Berkal,
  • Juan F. Navarro,
  • M. Y. Hamada,
  • Billel Semmar

摘要

The objective of this study is to examine the dynamic behavior of a conformable fractional-order predator–prey system with a Holling-III type functional response. The fractional-order system is transformed into a discrete model through a discretization process. The fixed points are analyzed for both their existence and uniqueness. We then assess the local stability of the two fixed points using linearization techniques, and use the center manifold theorem and bifurcation theory to identify conditions for period-doubling and Neimark–Sacker bifurcations. To verify our findings, we perform numerical simulations and compute the maximum Lyapunov exponents to confirm the presence of chaotic behavior.