Dynamics analysis of spatiotemporal discrete predator-prey model based on coupled map lattices

Wei Li; Qingkai Xu; Xingjian Wang; Chunrui Zhang; Wei Li; Qingkai Xu; Xingjian Wang; Chunrui Zhang

doi:10.3934/math.2025059

AIMS Mathematics

2025, Volume 10, Issue 1: 1248-1299. doi: 10.3934/math.2025059

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Research article

Dynamics analysis of spatiotemporal discrete predator-prey model based on coupled map lattices

1.
College of Mathematics, Northeast Forestry University, Harbin 150040, China
2.
College of Computer and Control Engineering, Northeast Forestry University, Harbin 150040, China

Received: 18 November 2024 Revised: 24 December 2024 Accepted: 02 January 2025 Published: 21 January 2025
MSC : 34C23, 37N25

In this paper, we explore the dynamic properties of discrete predator-prey models with diffusion on a coupled mapping lattice. We conducted a stability analysis of the equilibrium points, provided the normal form of the Neimark-Sacker and Flip bifurcations, and explored a range of Turing instabilities that emerged in the system upon the introduction of diffusion. Our numerical simulations aligned with the theoretical derivations, incorporating the computation of the maximum Lyapunov exponent to validate obtained bifurcation diagrams and elucidated the system's progression from bifurcations to chaos. By adjusting the self-diffusion and cross-diffusion coefficients, we simulated the shifts between different Turing instabilities. These findings highlight the complex dynamic behavior of discrete predator-prey models and provide valuable insights for biological population conservation strategies.
- predator-prey model,
- coupled map lattices,
- Neimark-Sacker bifurcation,
- Flip bifurcation,
- Turing instability,
- chaos
Citation: Wei Li, Qingkai Xu, Xingjian Wang, Chunrui Zhang. Dynamics analysis of spatiotemporal discrete predator-prey model based on coupled map lattices[J]. AIMS Mathematics, 2025, 10(1): 1248-1299. doi: 10.3934/math.2025059

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Abstract

In this paper, we explore the dynamic properties of discrete predator-prey models with diffusion on a coupled mapping lattice. We conducted a stability analysis of the equilibrium points, provided the normal form of the Neimark-Sacker and Flip bifurcations, and explored a range of Turing instabilities that emerged in the system upon the introduction of diffusion. Our numerical simulations aligned with the theoretical derivations, incorporating the computation of the maximum Lyapunov exponent to validate obtained bifurcation diagrams and elucidated the system's progression from bifurcations to chaos. By adjusting the self-diffusion and cross-diffusion coefficients, we simulated the shifts between different Turing instabilities. These findings highlight the complex dynamic behavior of discrete predator-prey models and provide valuable insights for biological population conservation strategies.

References

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