Control Analysis of Stochastic Lagging Discrete Ecosystems

In this paper, control analysis of a stochastic lagging discrete ecosystem is investigated. Two-dimensional stochastic hysteresis discrete ecosystem equilibrium points with symmetry are discussed, and the dynamical behavior of equilibrium points with symmetry and their control analysis is discussed. Using the orthogonal polynomial approximation theory, the stochastic lagged discrete ecosystems are approximately transformed as its equivalent deterministic ecosystem. Based on the stability and bifurcation theory of deterministic discrete systems, through mathematical analysis, asymptotic stability and Hopf bifurcation are existent in the ecosystem, constructing control functions, controlling the behavior of the system dynamics. Finally, the effects of different random strengths on the bifurcation control and asymptotic stability control are verified by numerical simulations, which validate the correctness and effectiveness of the main results of this paper.