Stability Analysis Of Predator - Prey Ecological Model With Random Excitation

This paper discusses the stability problem of two stochastic predation type ecos-ystem of toxin producing Phytoplankton-Zooplankton interactions and independent harvesting predation type ecosystem with the stochastic averaging principle. Our research and results mainly includes the following aspects:Firstly,the background, current situations and significance about the predation type ecosystem, the basic theoretical knowledge of Gaussian white noise and stationary colored noise are introduced, A detailed introduction to the stochastic averaging principle and Monte Carlo simulation which is used in the late thesis is also given.Secondly, the nonlinear dynamics theory is applied to analyze the equilibriums stability of toxin-producing Phytoplankton-Zooplankton interactions, then the stochastic Gauss white model is estabished. To explore noises effects on the stability of the ecosystem, with the assumption of weak disturbances, the stationary probability density functions for both species are obtained by applying the Stratonovich-Khasminskii averaging principle and boundary theory. The accuracy of the results obtained from theoretical method is demonstrated by those obtained from Monte Carlo simulation. Results obtained show that:the predator with smaller toxin is less stable when the system is disturbed by noises; the stronger the noise intensities are, the less stable the ecosystem will be.Thirdly, a stochastic model with corporating a prey-refuge and independent harvesting in either species is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically through the Markov approximation of stationary process and the averaging principle, then the prey-harvesting and colored noises effects on the stability of the ecosystem is studied. Effects on the ecosystem behaviors are evaluated:the ecosystem with smaller harvesting is less stable when the system is disturbed by noises; the narrower the band width is, the less stable the ecosystem will be, a narrower band width leads to a less stable system; a smaller correlation time leads to a more stable system.Considering the influence of random factor in the environment, the different system parameters and intensity of random perturbations can affect the stability of the system. The results show that the external random disturbance is one of the important factors that affect the steady state of the ecosystem.