ANALYSIS OF COMPLEX AND CHAOTIC PATTERNS NEAR A CODIMENSION-2 TURING-HOPF POINT IN A REACTION-DIFFUSION MODEL

We study a reaction-diffusion system of activator-inhibitor type, and characterize the resulting complex and chaotic spatio-temporal pattern s by their Lyapunov spectrum and by a Karhunen-Loeve decomposition int o empirical orthogonal eigenmodes. Different periodic patterns corresp onding to localized Hopf and Turing modes, and mixed modes including s ubharmonic spatio-temporal spiking are found near a codimension-2 bifu rcation point. The asymptotic patterns are preceded by transient spati o-temporal chaos, before the system abruptly locks into a periodic sta te in space and time. The Karhunen-Loeve decomposition is shown to be a powerful tool for extracting detailed quantitative information of co mplex space-time data.