A Food Chain Model with Ratio-dependent Functional Response, Impulsive Perturbations and Feedback Controls
Jian-wen Jia *
School of Mathematics and Computer Science, Shanxi Normal University , Shanxi, Linfen, 041004, China.
Jian-feng Liu
School of Mathematics and Computer Science, Shanxi Normal University , Shanxi, Linfen, 041004, China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a food chain system with ratio-dependent functional response, impulses,feedback controls and delays is studied. By using the theorem of coincidence degree, homotopy invariance property and Lyapunov’s approach, a set of sufficient conditions for ensuring the existence and stability of positive periodic solutions of the system are derived. The results extend some recent works.
Keywords: Predator-prey system, Feedback controls, Impulses, Delays, Periodic solution, Coincidence degree.