The Limit Cycles of the Predator—Prey Ecosystem with Holling Functional Response
Author(s): Zhou Jin-shi
Pages: 15-24
Year: 1987 Issue: 4
Journal: Journal of Fujian Normal University(Natural Science Edition)
Keyword: Biomathematies; populations; system; limit cycles; stability;
Abstract: In this paper, the population model which the velocity of the preying rate of the predator population changes when quantities of the prey population increase is concerned. We get the sufficient and necessary condition for there to exist a unique positive equilibrium for the ecosystem and the criteria under which such a system is globally stable. We also have the result that the Ecosystem can exist at least one limit cycle or at least two limit cycles. Therefore, the criteria for which predator population disappears or two populations coexist to reach"Ecology Balance"is developed.
Pages: 15-24
Year: 1987 Issue: 4
Journal: Journal of Fujian Normal University(Natural Science Edition)
Keyword: Biomathematies; populations; system; limit cycles; stability;
Abstract: In this paper, the population model which the velocity of the preying rate of the predator population changes when quantities of the prey population increase is concerned. We get the sufficient and necessary condition for there to exist a unique positive equilibrium for the ecosystem and the criteria under which such a system is globally stable. We also have the result that the Ecosystem can exist at least one limit cycle or at least two limit cycles. Therefore, the criteria for which predator population disappears or two populations coexist to reach"Ecology Balance"is developed.
Related Articles