Stationary distribution and boundary control of a stochastic reaction–diffusion population-toxicant model in aquatic habitats

An Ma, Jing Hu, Yuming Chen, Ming Ye and Qimin Zhang

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 246, issue C, 727-745

Abstract: This paper introduces a population-toxicant model consisting of a system of stochastic partial differential equations formulated for aquatic environments. Utilizing an innovative variable transformation, the well-posedness of the system is established. Within the Lyapunov method framework, the existence and uniqueness of the stationary distribution of the global positive solution are obtained. Mathematical results reveal that the stability of the system is maintained by spatial diffusion but negatively affected by environmental white noises. By developing an intermittent boundary controller, criteria are derived for ensuring mean square exponential stabilization, which is based on Poincaré’s inequality and the spatial integral functional method. The criteria are further analyzed to understand the impacts of control gain, diffusion term, and minimum control proportion on exponential stability. Numerical examples are provided to validate the theoretical findings.

Keywords: Stochastic population-toxicant model; Spatial diffusion; Stationary distribution; Intermittent boundary controller; Exponential stabilization (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:246:y:2026:i:c:p:727-745

DOI: 10.1016/j.matcom.2026.03.001

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