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

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Titel: Dynamics analysis of spatiotemporal discrete predator-prey model based on coupled map lattices
Autoren: Wei Li, Qingkai Xu, Xingjian Wang, Chunrui Zhang
Quelle: AIMS Mathematics, Vol 10, Iss 1, Pp 1248-1299 (2025)
Verlagsinformationen: American Institute of Mathematical Sciences (AIMS), 2025.
Publikationsjahr: 2025
Schlagwörter: flip bifurcation, chaos, QA1-939, predator-prey model, turing instability, neimark-sacker bifurcation, Mathematics, coupled map lattices
Beschreibung: 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.
Publikationsart: Article
ISSN: 2473-6988
DOI: 10.3934/math.2025059
Zugangs-URL: https://doaj.org/article/83707ac2b50341f4ad40d2a5c246ef05
Dokumentencode: edsair.doi.dedup.....e95338b6c57e3433855f2e92c43d9bab
Datenbank: OpenAIRE
Beschreibung
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.
ISSN:24736988
DOI:10.3934/math.2025059