Evolution of predator–prey systems described by a Lotka–Volterra equation under random environment
Evolution of predator–prey systems described by a Lotka–Volterra equation under random environment
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DOI：
10.1016/j.jmaa.2005.11.009
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发表时间：
2006-11
影响因子：
1.3
通讯作者：
Y. Takeuchi;N. Du;N. Hieu;K. Sato
中科院分区：
文献类型：
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作者：
Y. Takeuchi;N. Du;N. Hieu;K. Sato
本文研究了随机环境中由Lotka-Volterra方程描述的两个捕食者-食饵确定性系统组成的系统的演化。证明了在电报噪声的影响下，当两个系统的两个静止点不重合时，系统的所有正轨线总是以概率1从intR+2的任一紧集出去.在它们有共同的静止点的情况下，轨迹要么离开intR+2的任何紧致集，要么收敛到静止点。从任何紧集的轨迹逃逸意味着系统既不是永久的也不是耗散的。
In this paper, we consider the evolution of a system composed of two predator–prey deterministic systems described by Lotka–Volterra equations in random environment. It is proved that under the influence of telegraph noise, all positive trajectories of such a system always go out from any compact set of intR+2with probability one if two rest points of the two systems do not coincide. In case where they have the rest point in common, the trajectory either leaves from any compact set of intR+2or converges to the rest point. The escape of the trajectories from any compact set means that the system is neither permanent nor dissipative.