Article ID Journal Published Year Pages File Type
766798 Communications in Nonlinear Science and Numerical Simulation 2014 16 Pages PDF
Abstract

•Holling type III functional response reflect exactly interactions between vertebrates.•Adopt a modified analysis skill of papers [2] and [17].•Figures illustrate the permanence of the system from three different point of views.

An impulsive reaction–diffusion periodic food-chain system with ratio-dependent functional response is investigated in the present paper. Sufficient conditions for the ultimate boundedness and permanence of the food-chain system are established based on the comparison theory of differential equation and upper and lower solution method. By constructing appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are presented to verify our results. A discussion is given in the end of the paper.

Related Topics
Physical Sciences and Engineering Engineering Mechanical Engineering
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