Stability analysis of discrete ecological dynamical systems with composite stochastic parameters

In this paper, we investigate the stability analysis of random composite discrete power systems with random parameters. Firstly, by the orthogonal polynomial approximation of discrete random function in the Hilbert space, we convert two-dimensional discrete stochastic system into its equivalent deterministic system. Then, using two independent and identically distributed random variables, we construct the July criterion on the basis of mathematical analysis and the algebraic criterion in the asymptotic stability theory of discrete dynamical systems. Finally, we prove that the system is stable in part in its parameter plane, and the random intensity can cause a change in the stability region of the system. Furthermore, we give the numerical simulation to illustrate the correctness of the results in this paper.