Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (1): 16-27.

• Articles • Previous Articles     Next Articles

Stationary Patterns of a Leslie-Gower Type Three Species Model with Cross-Diffusions

 HU Guang-Ping, LI Xiao-Ling   

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044
  • Received:2011-04-20 Revised:2012-06-01 Online:2013-02-25 Published:2013-02-25
  • Supported by:

    国家自然科学基金(11026212)和南京信息工程大学基金(20100364)资助

Abstract:

This paper is concerned with a Leslie-Gower type three species model subject to the homogeneous Neumann boundary condition. We will show that under certain hypotheses, even though the unique positive equilibrium is asymptotically stable for the dynamics with diffusion, Turing instability can produce due to the presence of the cross-diffusion. In particular, we establish the existence of non-constant positive steady states of this system. The results indicate that cross-diffusion can create  stationary patterns.

Key words: Cross-diffusion, Predator-prey system, Priori estimates, Non-constant positive steady state

CLC Number: 

  • 35J48
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