Dynamics of stochastic diffusive coral reef ecosystems with Lévy noise.

Abstract

This paper was mainly concerned with the asymptotic dynamics of stochastic diffusive coral reef ecosystems with Lévy noise. First, we proved the well-posedness and energy estimates of solution. Second, under some suitable conditions, we proved the existence and uniqueness of weak pullback mean random attractors and invariant measures. Finally, a large deviation principle result for solutions of stochastic diffusive coral reef ecosystems with Lévy noise was obtained by a variational formula for positive functionals of a Poisson random measure and the method of weak convergence. Interestingly, this showed the effect of Lévy noise which can stabilize or destabilize systems, which was significantly different from the classical Brownian motion process.