Limit cycles in a prey-predator system
نویسندگان
چکیده
منابع مشابه
Limit cycles in predator-prey communities.
Essentially all models that have been proposed for predator-prey systems are shown to possess either a stable point equilibrium or a stable limit cycle. This stable limit cycle, an explicitly nonlinear feature, is commonly overlooked in conventional analyses of these models. Such a stable limit cycle provides a satisfying explanation for those animal communities in which populations are observe...
متن کاملMultiple limit cycles for predator-prey models.
We construct a Gause-type predator-prey model with concave prey isocline and (at least) two limit cycles. This serves as a counter-example to the global stability criterion of Hsu [Math. Biosci. 39:1-10 (1978)].
متن کاملA tale of two cycles distinguishing quasi-cycles and limit cycles in finite predator prey populations
M. Pineda-Krch ([email protected]), H. J. Blok and M. Doebeli, Dept of Zoology and Dept of Mathematics, Univ. of British Columbia, Vancouver, Canada BC V6T 1Z4. Present address for MP-K: Center for Animal Disease Modeling and Surveillance, Dept of Medicine and Epidemiology, School of Veterinary Medicine, Univ. of California, Davis, CA 95616, USA. U. Dieckmann, Evolution and Ecology Program,...
متن کاملNonexistence of Limit Cycles in a Predator-prey System with a Sigmoid Functional Response
In this paper we consider a predator-prey system with a sigmoid functional response of the form ~ ( x ) = x n / ( a + x n ) , n > 1 . Following Sugie et al. results in [S] and 191, by taking advantage of Freedman and So's theorem in 131, we present a sufficient and necessary condition for the nonexistence of limit cycles of this system with n > 1.
متن کاملExistence of Limit Cycles in a Predator-prey System with a Functional Response
We consider the existence of limit cycles for a predator-prey system with a functional response. The system has two or more parameters that represent the intrinsic rate of the predator population. A necessary and sufficient condition for the uniqueness of limit cycles in this system is presented. Such result will usually lead to a bifurcation curve. 2000 Mathematics Subject Classification. 92D40.
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1993
ISSN: 0893-9659
DOI: 10.1016/0893-9659(93)90042-l