一类随机Harrison型捕食与被捕食系统的稳定性分析

研究了一种具有Harrison功能反应函数的随机捕食与被捕食系统模型,该模型中捕食者的死亡率和被捕食者的增长率受到独立同分布的两对称三值噪声的影响.文中运用线性化理论和Shapiro-Loginov方程给出了系统扰动的一阶矩和二阶矩方程,并用Routh-Hurwitz稳定性判据给出了系统稳定的条件.研究表明噪声强度σ和噪声自相关时间τ均对系统的稳定性有影响.当噪声强度充分大或噪声自相关时间足够小都能使系统失稳.最后通过数值方法,验证了分析结果的准确性.

Stability analysisof a stochastic predator-prey model with Harrison functional response

The stability of a Harrison predator-prey model driven by symmetric trichotomous noises is studied in this paper. Using the Shapiro Loginov formula, the first order and second order moments of the linearized system are obtained. Then, the stability condition of the Harrison predator-prey model is given by using Routh Hurwitz stability criterion. It is found that the stability of the system depends on the noise intensities and correlation time. Finally, some numerical results are performed to support the theoretical analyses.