Study On Periodic Solution Of A Class Of State-dependent Impulsive Cooperative System

It is well-known that the theory of impulsive differential equation is not only richer than the corresponding theory of differential equation but also represent a more natural framework for mathematical modelling of many real world phenomena. In this paper, we investigate a class of state-dependent impulsive cooperative system. First, by using geometric analysis and the successor function, we find the sufficient condition for exisence the order 1 periodic solution of the system. Secondly, we analyze a particular state-dependent impulsive system, we show that there exist the order 1 and order 2 periodic solutions, then use the Analogue of the Poincare Criterion, we also show that the order 1 periodic solution of the system is orbitally asymptotically stable under some conditions. The results show that harmful life can always be no more than the economic harm level in given conditions, so people in the agricultural production can obtain the greatest profit. The method, which is used to prove the order 1 periodic solution of the system exists in this paper, can be extended to other state-dependent pulse feedback model.