, Volume 19, Issue 4, pp 801-822

Periodicity and Stability in Periodic n-Species Lotka-Volterra Competition System with Feedback Controls and Deviating Arguments

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Abstract

By using the method of coincidence degree and Lyapunov functional, a set of easily applicable criteria are established for the global existence and global asymptotic stability of strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterra competition system with feedback controls and several deviating arguments. The problem considered in this paper is in many aspects more general and incorporate as special cases various problems which have been studied extensively in the literature. Moreover, our new criteria, which improve and generalize some well known results, can be easily checked.

Supported by the National Natural Sciences Foundation of P. R. China (No. 10171010 and 10201005), the Key Project on Science and Technology of the Education Ministry of P. R. China (No. Key 01061) and the Science Foundation of Jilin Province of P. R. China for Distinguished Young Scholars