# American Institute of Mathematical Sciences

December  2011, 15(3): 849-865. doi: 10.3934/dcdsb.2011.15.849

## Stability of positive constant steady states and their bifurcation in a biological depletion model

 1 College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China, China

Received  October 2009 Revised  August 2010 Published  February 2011

This paper is concerned with a biological depletion model in a bounded domain. The stability of the positive constant steady states is discussed. In one dimensional case, we make a detailed description for the global bifurcation structure from two positive constant solutions. The result indicates that if $d$ is properly small, the system has at least one non-constant positive steady-state. The main tools used here include the stability theory, bifurcation theory and simulations. From extensive numerical simulations, the predictions from linear theory are confirmed and the influence of parameters $d,D,\sigma$ on these patterns is depicted.
Citation: Yan'e Wang, Jianhua Wu. Stability of positive constant steady states and their bifurcation in a biological depletion model. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 849-865. doi: 10.3934/dcdsb.2011.15.849
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