Acta mathematica scientia,Series A ›› 2005, Vol. 25 ›› Issue (1): 57-66.

• Articles • Previous Articles     Next Articles

Stability and Hopf Bifurcation of an Eco epidemiological Model with Delays

 SONG Xin-Yu, XIAO Yan-Ni, CHEN Lan-Sun   

  1. 信阳师范学院数学系 河南信阳 464000 中国科学院数学与系统科学研究院 北京 100080
  • Online:2005-02-25 Published:2005-02-25
  • Supported by:

    国家自然科学基金(10471117)和河南省高校杰出科研人才创新工程项目

Abstract:

 A system of retarded functional differential equations is proposed as a predatorprey model with disease in the prey. The  invariance of non negativity, nature of boundary equilibria  and global stability are analyzed. The authors show that positive equilibrium is locally asymptotically stable when time delays τ=τ\-1+τ\-2 is suitable small,  while a loss of stability by a Hopf bifurcation can occur as the delays increase.

Key words: Predator prey model, Global stability;  , Hopf bifurcation.

CLC Number: 

  • 34D20
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