# American Institute of Mathematical Sciences

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May  2016, 21(3): 909-918. doi: 10.3934/dcdsb.2016.21.909

## Dynamics in a Rosenzweig-Macarthur predator-prey system with quiescence

 1 School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, China 2 Department of Basic Science, Harbin University of Commerce, Harbin, Heilongjiang, 150001, China

Received  July 2015 Revised  September 2015 Published  January 2016

A system of four coupled ordinary differential equations is considered, which are coupled through migration of both prey and predator model with logistic type growth. Combined effect of quiescence provides a more realistic way of modeling the complex dynamical behavior. The global stability and Hopf bifurcation solutions are investigated.
Citation: Jinfeng Wang, Hongxia Fan. Dynamics in a Rosenzweig-Macarthur predator-prey system with quiescence. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 909-918. doi: 10.3934/dcdsb.2016.21.909
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