%0 Journal Article
%T 具基因突变的周期脉冲捕食食饵系统的动力学行为研究&lt;br&gt;Dynamic Behavior of a Periodic Impulsive Predator-Prey System with a Genetic Mutational Effect
%A 李雅芝
%A 熊梅&lt
%A br&gt
%A LI Ya-zhi
%A XIONG Mei
%J 西南大学学报(自然科学版)
%D 2018
%R 10.13718/j.cnki.xdzk.2018.03.012
%X 研究了一个周期脉冲捕食-食饵系统.首先得到了系统的一个不变区域；其次得到了系统的平凡周期解和捕食者灭绝周期解的存在性；最后通过数值模拟探讨食饵基因突变率对系统动力学行为的影响，结果显示存在两个阈值&lt;i&gt;θ&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;sup&gt;*&lt;/sup&gt;和&lt;i&gt;θ&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;*&lt;/sup&gt;，使得突变率&lt;i&gt;θ&lt;/i&gt;在不同的取值范围时，系统分别出现全部种群灭绝、捕食者种群灭绝和全部种群持续生存3种情况，也即食饵种群的基因突变率对种群的动力学行为有重要影响.&lt;br&gt;This paper deals with a periodic impulsive predator-prey system. Firstly, an invariant region for the system is obtained. Secondly, the existence of the trivial periodic solution and the predator-eradication periodic solution are obtained. Finally, the influence of mutation rate of prey on the dynamics of the system is discussed through numerical simulation. The results show that there exist two critical values, i.e. &lt;i&gt;θ&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;sup&gt;*&lt;/sup&gt; and &lt;i&gt;θ&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;*&lt;/sup&gt;, which results in three different situations in the system according to the different ranges of mutation rate &lt;i&gt;θ&lt;/i&gt;, namely, all the population dies out, the predator population becomes extinct and all the population survives persistently. In other words, genetic mutation rate has a great influence on the dynamics behavior of the system
%K 周期捕食-食饵系统
%K 基因突变
%K 脉冲
%K 灭绝
%K 持续生存&lt
%K br&gt
%K periodic predator-prey system
%K gene mutation
%K impulse
%K extinction
%K permanence
%U http://xbgjxt.swu.edu.cn/jsuns/html/jsuns/2018/3/201803012.htm