两浮游植物离散竞争模型的动力学分析

Dynamics analysis of a discrete two-species competitive system

讨论一类具有毒素的两种群离散竞争模型,利用差分不等式的有关理论及技巧性的计算,分别探讨了毒素对系统持久性、全局吸引性和绝灭性的影响.结果表明,毒素抑制率b1(n),b2(n)对系统的持久性没有影响,但是当毒素抑制率bi(n)(i=1,2)足够大时,系统的全局吸引性就会被破坏.同时还说明当毒素抑制率b2(n)足够小时,x1一定绝灭.

This paper studies a class of discrete two-species competitive system with the effect of toxic substances. Using the theory of difference inequality and some calculation technique, the influence of toxic substances on the permanence, global attractivity and extinction of the system are discussed respectively. The results show that the toxin inhibition rate has no effect on the permanence of the system. However, when the toxin inhibition rates are sufficiently large, the global attractivity will be destroyed. Meanwhile, when the toxin inhibition rate is small enough, x1 must go a species extinction.