Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 19, Issue 1, Pages 173-188Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2013.05.030
Keywords
Reaction-diffusion; Ratio-dependent functional response; Food-chain system; Permanence; Stability
Categories
Funding
- National Basic Research Program of China [2010CB732501]
- National Natural Science Foundation of China [NSFC-60873102]
- Zhejiang Provincial Natural Science Foundation of China [LQ13A010023]
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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. (c) 2013 Elsevier B.V. All rights reserved.
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