Research on the Stochastic Hopf Bifurcation of the Shallow Lake Ecosystem with Stochastic Excitation

摘要

Establishing the model of the shallow lake ecosystem with stochastic excitation, with the stochastic averaging method and nonlinear dynamic theory, the model of the shallow lake ecosystem with stochastic excitation was simplified. Based on the Stratonovich-Khasminiskii stochastic average principle and Oseledec multiplicative ergodic theory. We studied the stochastic Hopf bifurcation behavior with the FPK method. The results showed that the bifurcation behavior of the stochastic system is different from the bifurcation behavior of the deterministic system. The effect of stochastic factors can make the stability of the system appear change. A pseudo-random noise can make the system appear regime shift. The bifurcation value of the system shifts.