# American Institute of Mathematical Sciences

June  2015, 20(4): 1117-1134. doi: 10.3934/dcdsb.2015.20.1117

## Dynamics of the density dependent and nonautonomous predator-prey system with Beddington-DeAngelis functional response

 1 Department of Mathematics and Information, Henan University of, Economics and Law, Zhengzhou, China 2 College of Science and Engineering, Aoyama Gakuin University, Sagamihara, 2525258

Received  March 2014 Revised  June 2014 Published  February 2015

We investigate the dynamics of a non-autonomous and density dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered. First, we derive a sufficient condition of permanence by comparison theorem, at the same time we propose a weaker condition ensuring some positive bounded set to be positive invariant. Next, we obtain two existence conditions for positive periodic solution by Brouwer fixed-point theorem and by continuation theorem, where the second condition is weaker than the first and gives the existence range of periodic solution. Further we show the global attractivity of the bounded positive solution by constructing Lyapunov function. Similarly, we have sufficient condition of global attractivity of boundary periodic solution.
Citation: Haiyin Li, Yasuhiro Takeuchi. Dynamics of the density dependent and nonautonomous predator-prey system with Beddington-DeAngelis functional response. Discrete & Continuous Dynamical Systems - B, 2015, 20 (4) : 1117-1134. doi: 10.3934/dcdsb.2015.20.1117
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##### References:
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