Study On Dynamic Of Stochastic Reaction Diffusion Mussel-algae Model

Since 1990,the famous British biologist Turing's pioneering work:"Using a chemical substance to react with each other and cross-space system to explain the main phenomenon of morphogenesis in biology",as a result,the reactive diffusion mussel-algae model has attracted more and more researchers' attention.However,in the actual ecological environment,the ecosystem is inevitably affected by various stochastic factors,therefore,it is of practical significance to study the dynamic of the reactive diffusion mussel-algae model affected by environmental noise.This article will use probability theory,stochastic dynamic system and stochastic analysis to study the dynamic of the stochastic reaction diffusion mussel-algae model.The first chapter mainly introduces the related research background and significance of the stochastic reaction diffusion mussel-algae model,as well as some preliminary knowledge used in this paper,at the same time,it also further introduces the main content of this dissertation and its framework structure.The second chapter mainly studies the stability and ergodicity of the stochastic reaction diffusion mussel-algae model.First,using relevant knowledge such as the principle of compression mapping,under the condition that the interaction strength is sufficiently small,it is proved that there is a unique global positive solution for the stochastic reaction diffusion mussel-algae model;Secondly,using the comparison theorem and convergence semigroup theories,the conditions for the extinction and mean squ'are stability of the stochastic reaction diffusion mussel-algae model were obtained;Finally,using analytical methods and dual semigroups and other methods,the Markov property and invariant measure of the solution to the stochastic reaction diffusion mussel-algae model are proved.Numerical results show that under certain conditions,noise can not only affect the extinction of the reactive diffusion mussel-algae model,but also affect the stability of the reactive diffusion mussel-algae model.The third chapter mainly studies the exponential stability and weak recurrence of the stochastic reaction diffusion mussel-algae model.First,using Lebesgue control convergence theorem and pseudo-contraction semigroups and other related knowledge,it is proved that the weak solution of the stochastic reaction diffusion mussel-algae model is exponentially stable in the mean square sense;Secondly,by cleverly constructing the Lyapunov function,using techniques such as bounded linear operators and Gronwall inequality,the weak solution of the stochastic reaction diffusion mussel-algae model is finally bounded exponentially in the mean square sense;Finally,under the condition that the exponential is ultimately bounded in the sense of mean square,the theory of strong Markov property,collinear compactness and Chebyshev's inequality is further used to prove the weak recurrence of the solution of the stochastic reaction diffusion mussel-algae model.