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Bifurcations and pattern formation in a generalized Lengyel–Epstein reaction–diffusion model

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  • Mansouri, Djamel
  • Abdelmalek, Salem
  • Bendoukha, Samir

Abstract

This paper investigates the formation of spatial patterns in a general reaction–diffusion system based on the Lengyel–Epstein CIMA model. By analyzing the properties of the system’s unique positive equilibrium in the ODE and PDE cases, we establish the existence of non–constant steady state solutions thereby confirming the existence of Turing instability. Hopf–bifurcation analysis of the system show the existence of periodic solutions in the absence and presence of diffusion. Numerical simulations are presented to validate the theoretical results of the paper.

Suggested Citation

  • Mansouri, Djamel & Abdelmalek, Salem & Bendoukha, Samir, 2020. "Bifurcations and pattern formation in a generalized Lengyel–Epstein reaction–diffusion model," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305363
    DOI: 10.1016/j.chaos.2019.109579
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    Cited by:

    1. Yangyang Shao & Yan Meng & Xinyue Xu, 2022. "Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect," Mathematics, MDPI, vol. 10(9), pages 1-15, May.

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