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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 849 - 865, Volume 15, Issue 3, May 2011      doi:10.3934/dcdsb.2011.15.849

 
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Yan'e Wang - College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China (email)
Jianhua Wu - College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China (email)

Abstract: 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.

Keywords:  Depletion model, stability, bifurcation, simulation.
Mathematics Subject Classification:  Primary: 35K57, 92D25.

Received: October 2009;      Revised: August 2010;      Available Online: February 2011.

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