Stochastic stability and Hopf bifurcation analysis of a singular bio-economic model with stochastic fluctuations

Abstract

In this paper, we study a class of singular stochastic bio-economic models described by differential-algebraic equations due to the influence of economic factors. Simplifying the model through a stochastic averaging method, we obtained a two-dimensional diffusion process of averaged amplitude and phase. Stochastic stability and Hopf bifurcations can be analytically determined based on the singular boundary theory of diffusion process, the Maximal Lyapunov exponent and the invariant measure theory. The critical value of the stochastic Hopf bifurcation parameter is obtained and the position of Hopf bifurcation drifting with the parameter increase is presented as a result. Practical example is presented to verify the effectiveness of the results.