一类具有Beddington-DeAngelis功能性反应随机模型的数值模拟

摘要

考虑被捕食者的生长率和捕食者的死亡率分别受到高斯白噪声和泊松白噪声扰动的情况，建立了具有BDA功能性反应的三种群密度的随机演化模型，并利用Milstein方法对系统进行了离散化处理；通过计算机代数Matlab编程，完成了确定系统及随机系统的数值模拟。结果表明：在随机扰动强度很小的情况下，系统会产生有界的混沌状态。%Considering Poisson white noise and Gauss white noise into the intrinsic grow rate of prey and the death rate of predators, a stochastic system of three population densities with Beddington-DeAngelis functional response is established. Then Milstein method is used to make stochastic system discrete and programs is compiled with computer algebra Matlab to finish the analysis. Numerical simulations of deterministic system and stochastic system certifiy the result obtained. The results demonstrate that a bounded chaotic attractor would occur in the stochastic system if the noises are sufficiently small.