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Nonlinear dynamics and spatiotemporal patterns of a delayed reaction-diffusion system on a square domain
Phys. Rev. E 113, 014212 – Published 20 January, 2026
DOI: https://doi.org/10.1103/sdv2-lf44
Abstract
In this work, we analyze the pattern formation in a delayed reaction-diffusion system on a square domain. Using bifurcation theory and amplitude equations, we reveal symmetry-breaking dynamics near criticality, including rotating waves and quasiperiodic solutions. We apply this framework to both a Ginzburg-Landau equation and a delayed predator-prey model, explaining spatiotemporal patterns such as standing and spiral waves. The main contributions are the derivation of explicit normal forms for systems with spatial symmetry and the development of a predictive approach that links model parameters to the selection and stability of nonlinear patterns.
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