Abstract
Abstract In this paper, we consider a nonautonomous two-species impulsive competitive system with infinite delays. By the impulsive comparison theorem and some mathematical analysis, we investigate the permanence, extinction and global attractivity of the system, as well as the influence of impulse perturbation on the dynamic behaviors of this system. For the logistic type impulsive equation with infinite delay, our results improve those of Xuxin Yang, Weibing Wang and Jianhua Shen [Permanence of a logistic type impulsive equation with infinite delay, Applied Mathematics Letters, 24(2011), 420-427]. For the corresponding nonautonomous two-species impulsive competitive system without delays, we discuss its permanence, extinction and global attractivity, which weaken and complement the results of Zhijun Liu and Qinglong Wang [An almost periodic competitive system subject to impulsive perturbations, Applied Mathematics and Computation, 231(2014), 377-385].
Highlights
The logistic system is considered to be one of the most important systems in mathematical ecology, and a great deal of research works have been done based on this system
By the impulsive comparison theorem and some mathematical analysis, we investigate the permanence, extinction and global attractivity of the system, as well as the in uence of impulse perturbation on the dynamic behaviors of this system
For the logistic type impulsive equation with in nite delay, our results improve those of Xuxin Yang, Weibing Wang and Jianhua Shen [Permanence of a logistic type impulsive equation with in nite delay, Applied Mathematics Letters, 24(2011), 420-427]
Summary
The logistic system is considered to be one of the most important systems in mathematical ecology, and a great deal of research works have been done based on this system. The authors discussed the permanence of system (1.2) under the following conditions: (H1) Π , i = , . According to Lemma 2.2, we obtain that lim sup xi(t)
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