Random attractors for a stochastic age-structured population model

In this paper, we are concerned about the existence of a random attractor for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) under a Dirichlet boundary condition. This equation models the spatial-temporal evolution of the mature individuals for a two-stage species whose juvenile and adults both diffuse under random perturbations. By adopting the random dynamical system theory together with the stochastic inequality technique, we first give a uniform estimate of the solution and then prove the asymptotic compactness of the random dynamic system generated by the SNDRDE and, subsequently, obtain the existence of a random attractor. Published under an exclusive license by AIP Publishing.

Automated summary

This paper focuses on the existence of a random attractor for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) under a Dirichlet boundary condition. By adopting the random dynamical system theory together with the stochastic inequality technique, the authors first provide a uniform estimate of the solution and then prove the asymptotic compactness of the random dynamic system generated by the SNDRDE. The existence of a random attractor is subsequently obtained.