一类捕食者-食饵共生互作离散耦合logistics模型的余维一分岔及Marotto混沌

Abstract

Abstract:

In this paper, we investigate bifurcation phenomena and Marotto's chaos in a class of discrete-time predator-prey mutualistic interaction logistics models. Firstly, applying the theory of polynomial complete discrimination systems to solve the corresponding high-order semi-algebraic system, we determine and present the topological classifications of each fixed point alongside its stability conditions. Secondly, based on the center manifold theorem and bifurcation theory, we further establish the parameter conditions under which the system undergoes transcritical and flip bifurcations in the corresponding non-hyperbolic cases. Additionally, we prove that the system possess snap-back repellers, thereby exhibiting chaos in the sense of Marotto. Finally, utilizing ${\tt Matlab R2024a}$ and ${\tt Maple 2024}$ for numerical simulations, we reconstruct the system's bifurcation processes and the evolutionary trajectories of chaotic behavior. The corresponding Lyapunov exponents further validate the accuracy of the aforementioned theoretical results.

Key words: coupled logistics model, polynomial complete discrimination system, bifurcation, Marotto's chaos, Lyapunov exponents

CLC Number:

O178

Kaiyue Zheng, Na Liu, Zhiheng Yu. Codimension-one Bifurcations and Marotto's Chaos in a Class of Discrete Coupled Predator-Prey Mutualistic Interaction Logistics Models[J].Acta mathematica scientia,Series A, 2026, 46(5): 1932-1950.

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Codimension-one Bifurcations and Marotto's Chaos in a Class of Discrete Coupled Predator-Prey Mutualistic Interaction Logistics Models

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