journal6 ›› 2003, Vol. 24 ›› Issue (2): 52-56.

• Mathematics • Previous Articles     Next Articles

Existence of Positive Periodic Solutions of Discrete Predator-Prey System With Infinite Delays


  1. (1.Dept.of Math.And Computer Science,Jishou University,Jishou 416000,Hunan China;2.College of Math.and Econometrics,Hunan University,Changsha 410082,Hunan China)
  • Online:2003-06-15 Published:2012-11-07

Abstract: The differential model of periodic Predator-Prey with three species is studied.The existence of positive periodic solution of this system with infinite delays is discussed by using the topologic theory.It is proved that the ample conditions for the existence of positive periodic solution of this system are as follows:(ⅰ)r-1a-32-r-3a-12exp(2r-2ω)>0;(ⅱ)r-1a-32-r-3a-12exp(2r-2ω)-r-2a-11a-32exp(2r-1ω)<0;(ⅲ)-a-32a-12r-1+a-32a-11r-2+a-21a-12r-3<0.

Key words: Predator-Prey system, positive periodic solution, infinite delays, discrete, topologic degree

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