Globally coupled chaotic maps and demographic stochasticity

The effect of noise on a system of globally coupled chaotic maps is considered. Demographic stochasticity is studied since it provides both noise and a natural definition for extinction. A two-step model is presented, where the intrapatch chaotic dynamics is followed by a migration step with global dispersal. The addition of noise to the already chaotic system is shown to dramatically change its behavior. The level of migration in which the system attains maximal sustainability is identified. This determines the optimal way to manipulate a fragmented habitat in order to conserve endangered species. The quasideterministic dynamics that appears in the large N limit of the stochastic system is analyzed. In the clustering phase, the infinite degeneracy of deterministic solutions emerges from the single steady state of the stochastic system via a mechanism that involves an almost defective Markov matrix.