Journal of South China University of Technology (Natural Science Edition) ›› 2007, Vol. 35 ›› Issue (8): 109-113.

• Mathematical Sciences • Previous Articles     Next Articles

Bifurcation and Stability of Steady -State Solutions to a Prey -Predator System

Fu Yi-ping1  Chen Xia2   

  1. 1. School of Mathematical Science , South China Univ. of Tech. , Guangzhou 510640 , Guangdong , China;2. Guangzhou Sixth High School , Guangzhou 510300 , Guangdong, China
  • Received:2006-09-08 Online:2007-08-25 Published:2007-08-25
  • Contact: 付一平(1962-)，女，教授，主要从事偏微分方程及其应用研究. E-mail:fuyiping@scut.edu.cn
  • About author:付一平(1962-)，女，教授，主要从事偏微分方程及其应用研究.
  • Supported by:

    国家自然科学基金资助项目( 10471047) ;广东省自然科学基金资助项目(04020077)

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Abstract:

Based on the bifurcation and perturbation theories , the existence and stability of the steady-state solutions to a prey-predator system of three species with cross-diffusion are discussed. Then , by taking the birth rate of the prey , the death rate of the first predator and the death rate of the second predator as the bifurcation parameters in order , the weak semi-trivial solution bifurcated from the trivial one , the strong semi-trivial solution bifurcated from the weak one and the nontrivial solution are all respectively obtained. The stability conditions for all the bifurcated solutions are finally presented in the paper.

Key words: cross-diffusion system, bifurcation, steady-state solution, asymptotic stability