No abstract

The transient nature of spatiotemporal chaos is examined in reaction-diffusion systems with coexisting stable states. We find the apparent asymptotic spatiotemporal chaos of the Gray-Scott system to be transient, with the average transient lifetime increasing exponentially with medium size. The collapse of spatiotemporal chaos arises when statistical spatial correlations produce a quasihomogeneous medium, and the system obeys its zero-dimensional dynamics to relax to its stable asymptotic state.

Dynamical noise, acting homogeneously in each time step, can enhance the stability of an unstable fixed point. However, if dynamical noise is added locally in state space, additional clear enhancement can be achieved, if this restriction is chosen properly. A systematic analysis of the influence of local and global dynamical noise on the residence time of an unstable state is presented, and optimal parameters for the stabilizing mechanisms are discussed. As a consequence, it is demonstrated that local dynamical noise can yield increased localization in deterministic diffusion models. ͓S1063-651X͑99͒08203-3͔

We introduce a measure to quantify spatiotemporal turbulence in extended systems. It is based on the statistical analysis of a coherent structure decomposition of the evolving system. Applied to a cellular excitable medium and a reaction-diffusion model describing the oxidation of CO on Pt(100), it reveals power-law scaling of the size distribution of coherent space-time structures for the state of spiral turbulence. The coherent structure decomposition is also used to define an entropy measure, which sharply increases in these systems at the transition to turbulence.