Retarded equations with infinite delays

1979 ◽  
pp. 157-193 ◽  
Author(s):  
Jack K. Hale
Keyword(s):  
Infinite Delays ◽  
Retarded Equations

On a periodic prey-predator system with infinite delays

2000 ◽  
Vol 15 (3) ◽  
pp. 267-272
Author(s):  
Li Yongkun ◽  
Xu Guitong
Keyword(s):  
Infinite Delays ◽  
Predator System

scholarly journals Dynamic of a nonautonomous two-species impulsive competitive system with infinite delays

2019 ◽  
Vol 17 (1) ◽  
pp. 776-794 ◽  
Author(s):  
Mengxin He ◽  
Zhong Li ◽  
Fengde Chen
Keyword(s):  
Comparison Theorem ◽  
Mathematical Analysis ◽  
Global Attractivity ◽  
Infinite Delay ◽  
Applied Mathematics ◽  
Almost Periodic ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
Impulsive Equation ◽  
Infinite Delays

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].

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

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