On a delay ratio-dependent predator-prey system with feedback controls and shelter for the prey  

作　　者：Changyou Wang Linrui Lit Yuqian Zhou Rui Li 

机构地区：[1]College of Applied Mathematics Chengdu University of Information Technology Chengdu,Sichuan 610225,P.R.China [2]Basic Courses Department,Institute of Disaster Prevention Sanhe,Hebei 065201,P.R.China [3]College of Automation Chongqing University of Posts and Telecommunzcations Chongqing 400065,P.R.China

出　　处：《International Journal of Biomathematics》2018年第7期287-316,共30页生物数学学报（英文版）

基　　金：the Sichuan Science and Technology Program(Grant No.2018JY0480)of China;the Natural Science Foundation Project of CQ CSTC (Grant No. cstc2015jcyjBX0135) of China;the Science Fund for Distinguished Young Scholars(cstc2014jc yjjq40004) of China;the Scientific Research Plan Projects for Higher Schools in Hebei Province(Grant No.Z2017047) of China;the Postdoctoral Science Foundation(Grant No.2016m602663)of China;the National Nature Science Fund (Project No.61503053) of China.

摘　　要：In this paper,a class of three-species multi-delay Lotka-Volterra ratio-dependent predator-prey model with feedback controls and shelter for the prey is considered.A set of easily verifiable sufficient conditions which guarantees the permanence of the system and the global attractivity of positive solution for the predator-prey system are established by developing some new analysis methods and using the theory of differentim inequalities as well as constructing a suitable Lyapunov function.Furthermore,some conditions for the existence,uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques.In addition,some numerical solutions of the equations describing the system are given to show that the obtained criteria are new,general,and easily verifiable.Finally,we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources,and obtain some new interesting dynamical behaviors of the system.At the same time,the influence of the delays and shelters on the dynamics behavior of the system is also considered by solving numerically the predator-prey models.

关 键 词：PREDATOR-PREY model feedback control DELAY PERMANENCE attractive periodic solution 

分 类 号：G[文化科学]