Dynamics analysis of a nonlinear controlled predator–prey model with complex Poincaré map
Articles
Huidong Cheng
Shandong Foreign Affairs Vocational University
Xin Zhang
Shandong University of Science and Technology
Tonghua Zhang
Swinburne University of Technology
Jingli Fu
Zhejiang Sci-Tech University
Published 2024-05-01
https://doi.org/10.15388/namc.2024.29.34680
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Keywords

nonlinear feedback control
precise pulse and phase set
periodic solution
Poincaré map

How to Cite

Cheng, H. (2024) “Dynamics analysis of a nonlinear controlled predator–prey model with complex Poincaré map”, Nonlinear Analysis: Modelling and Control, 29(3), pp. 466–487. doi:10.15388/namc.2024.29.34680.

Abstract

In this paper, we propose a class of predator–prey models with nonlinear state-dependent feedback control in the saturated state. The nonlinear state impulse control leads to a diversity of pulse and phase sets such that the Poincaré map built on the corresponding phase sets behaves like the single-peak function and multi-peak function with multiple discontinuities. We start our study by analyzing the exact pulse and phase sets of models under various cases generated by the dependent parameter space of nonlinear state feedback control, then construct the Poincaré map that is followed by investigating their monotonicity, continuity, concavity, and immobility properties. We also explore the existence, uniqueness, and sufficient conditions for the global stability of the order-1 periodic solutions of the systems. Numerical simulations are carried out to illustrate and reveal the biological significance of our theoretical findings.

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