Transient spatiotemporal chaos in reaction-diffusion networks

Complex transient dynamics is reported in various extended systems, including transient turbulence in shear flows, transient spatiotemporal chaos in reaction- diffusion models, and non-chaotic irregular transient dynamics in neural networks. The asymptotic stability is difficult to determine since the transient lifetime typically increases exponentially with the system size. Our studies show that transient spatiotemporal chaos is extensive in various reaction- diffusion systems; the Lyapunov dimension increases linearly with the network size. A master stability analysis provides insight into the asymptotic stability in the Baer- Eiswirth and the Gray-Scott systems. The asymptotic state is characterized by negative transverse Lyapunov exponents on the attractor of the invariant synchronization manifold. The average lifetime depends on the number of transverse directions that are unstable along a typical excitation cycle.