Oscillating Turing patterns, chaos and strange attractors in a reaction–diffusion system augmented with self- and cross-diffusion terms

Benjamin Aymard

Chaos, Solitons & Fractals, 2025, vol. 194, issue C

Abstract: In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and orbits of the latter. Special attention is paid to accuracy, a necessary condition when one wants to catch periodic orbits and to perform their linear stability analysis via Floquet multipliers. Bifurcations with respect to a single control parameter are studied in four different regimes of diffusion: linear diffusion, self-diffusion for each of the two species, and cross-diffusion. Key observations are made: development of original Turing patterns, supercritical Hopf bifurcations leading to oscillating patterns and period doubling cascades leading to chaos. Eventually, original strange attractors are reported in phase space.

Keywords: Self-diffusion; Cross-diffusion; Turing instability; Hopf bifurcation; Floquet theory; Period doubling cascade; Chaos; Strange attractors (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001948

DOI: 10.1016/j.chaos.2025.116181

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