Affiliation:
1. School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China
Abstract
In this paper, three competitive systems with different kinds of state-dependent control are presented and investigated. The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory, and the stability of the order-1 periodic solution of each system is also given. Besides, sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincaré criterion, respectively. Finally, numerical simulations are carried out to verify the theoretical results.
Funder
the National Natural Science Foundation of China
Science and Technology Department of Henan Province
Nanhu Scholars Program for Xinyang Normal University
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modeling and Simulation
Cited by
13 articles.
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