View in EDS

Spatially Nonhomogeneous Neimark–Sacker Bifurcation and New Pattern Formation Mechanism in a Spatiotemporally Discrete Predator–Prey System.

Saved in:
Bibliographic Details
Title: Spatially Nonhomogeneous Neimark–Sacker Bifurcation and New Pattern Formation Mechanism in a Spatiotemporally Discrete Predator–Prey System.
Authors: Huang, Tousheng1 (AUTHOR) tous_huang@ncepu.edu.cn, Hu, Chaofan1 (AUTHOR), Yang, Haotian1 (AUTHOR), Zheng, Jincheng1 (AUTHOR)
Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Sep2026, Vol. 36 Issue 11, p1-43. 43p.
Subjects: Bifurcation theory, Pattern formation (Physical sciences), Dynamical systems, Reaction-diffusion equations, Nonlinear mechanics, Predation, Spatiotemporal processes, Computer simulation
Abstract: This study explores the spatiotemporal dynamics of a discrete reaction–diffusion predator–prey system, with a focus on the spatially nonhomogeneous Neimark–Sacker bifurcation. We rigorously derive the normal form and theorem of the Neimark–Sacker bifurcation, extending the analysis to a two-dimensional space domain. The bifurcation theorem is applied to a spatiotemporally discrete Holling-II predator–prey system. The results uncover a sequence of Neimark–Sacker bifurcation points and the emergence of spatially nonhomogeneous quasi-periodic solutions. Numerical simulations validate the theoretical predictions and illustrate the self-organization of dynamic patterns induced by the bifurcation. Moreover, numerical results suggest that the interplay of multiple spatially nonhomogeneous quasi-periodic modes can produce complex spatiotemporal structures, such as fragmented mosaics and spiral waves. This work provides insights into new nonlinear mechanisms underlying complexity in discrete systems, offering a robust framework for analyzing predator–prey interactions in fragmented habitats. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
Abstract:This study explores the spatiotemporal dynamics of a discrete reaction–diffusion predator–prey system, with a focus on the spatially nonhomogeneous Neimark–Sacker bifurcation. We rigorously derive the normal form and theorem of the Neimark–Sacker bifurcation, extending the analysis to a two-dimensional space domain. The bifurcation theorem is applied to a spatiotemporally discrete Holling-II predator–prey system. The results uncover a sequence of Neimark–Sacker bifurcation points and the emergence of spatially nonhomogeneous quasi-periodic solutions. Numerical simulations validate the theoretical predictions and illustrate the self-organization of dynamic patterns induced by the bifurcation. Moreover, numerical results suggest that the interplay of multiple spatially nonhomogeneous quasi-periodic modes can produce complex spatiotemporal structures, such as fragmented mosaics and spiral waves. This work provides insights into new nonlinear mechanisms underlying complexity in discrete systems, offering a robust framework for analyzing predator–prey interactions in fragmented habitats. [ABSTRACT FROM AUTHOR]
ISSN:02181274
DOI:10.1142/S0218127426501439