The Complexity Analysis Of Several Kinds In Stochastic Bio-economic Model

This paper studies the problems of several kinds of stochastic bio-economic model.These stochastic bio-economic models are simplified to some Ito equations by the stochastic averaging method.The stochastic stability and bifurcation are discussed based on the system's maximal Lyapunov exponent,invariant measure theory of dynamic systems and the singular boundary theory of the diffusion process for the system.Three kinds of bio-economic models are systematically analyzed,one is the stochastic bio-economic model with stage-structuring,the capture effort is a constant.Another is a differential algebraic bio-economic model with stage-structured and stochastic fluctuations,the capture effort is a variable.The first model's dynamic analysis is the basis of the second model which is the optimization and perfection.Finally,the singularly induced bifurcation of the third stochastic bio-economic model is analyzed,which is the extension of the established differential-algebraic equation model for singularly induced bifurcation analysis.By analyzing the model,it is found that the position of the random Hopf bifurcation will increase with ?3,and the expression of ?3 can be seen to increase with the external excitations ?1,?2.At present,the analysis of the singular induced bifurcation of stochastic differential algebraic bio-economic model is few.In this paper,the singular induced bifurcation of stochastic systems is further studied by numerical simulation,and some results are obtained.This is a big breakthroughs.The research work in this paper shows that environmental fluctuation plays an important role in the stability of the system.