具有Markov切换的随机Lotka-Volterra模型的股东种群共生性研究

Symbiosis on stochastic Lotka-Volterra shareholder competitive system with Markov switching

借鉴生态种群系统理论,考查股东收益增长率受到外部经济环境扰动的随机非自治LotkaVolterra股东种群竞争模型,采用Markov切换的方式研究该股东种群系统的共生性。运用比较原理给出股东种群系统在切换状态下的随机共生性的充分性条件,通过构造Lyapunov函数的方法揭示股东种群系统在任意的切换状态下的静态分布。数值模拟验证了主要结果。

Based on the ecology population system theory, consider a stochastic non-autonomous Lotka- Volterra shareholder competitive system in which shareholder＇ s returns rate is randomly disturbed by external economy environment. The symbiosis on Lotka-Voherra shareholder competitive system is mainly studied by Markov switching. By applying comparison principle, some sufficient conditions for stochastic symbiosis on system are established in the swtich-state. Furthermore, by using Lyapunov function method, a stationary distribution of system is investigated in any swtich-state. Finally, numerical simulation is carried out to support the theoretical results.