Tristable Phenomenon in a Predator-Prey System Arising from Multiple Limit Cycles Bifurcation

Jiao Jiang; Wenjing Zhang; Pei Yu

doi:10.1142/S0218127420501291

Tristable Phenomenon in a Predator-Prey System Arising from Multiple Limit Cycles Bifurcation

Jiao Jiang, Wenjing Zhang, Pei Yu

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider a predator-prey system with Holling type III ratio-dependent functional response. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. In particular, we show that the ratio-dependent predator-prey system can exhibit multiple limit cycles due to Hopf bifurcation, giving rise to coexistence of stable equilibria and stable periodic solutions. These solutions may reveal some new type of patterns of complex dynamical behaviors in predator-prey systems.

Original language	English
Article number	2050129
Journal	International Journal of Bifurcation and Chaos
Volume	30
Issue number	9
DOIs	https://doi.org/10.1142/S0218127420501291
State	Published - Jul 1 2020

Keywords

Holling type functional response
Hopf bifurcation
Predator-prey system
bistable, tristable
focus value
limit cycle
normal form

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10.1142/S0218127420501291

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title = "Tristable Phenomenon in a Predator-Prey System Arising from Multiple Limit Cycles Bifurcation",

abstract = "In this paper, we consider a predator-prey system with Holling type III ratio-dependent functional response. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. In particular, we show that the ratio-dependent predator-prey system can exhibit multiple limit cycles due to Hopf bifurcation, giving rise to coexistence of stable equilibria and stable periodic solutions. These solutions may reveal some new type of patterns of complex dynamical behaviors in predator-prey systems. ",

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AU - Jiang, Jiao

AU - Zhang, Wenjing

AU - Yu, Pei

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N2 - In this paper, we consider a predator-prey system with Holling type III ratio-dependent functional response. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. In particular, we show that the ratio-dependent predator-prey system can exhibit multiple limit cycles due to Hopf bifurcation, giving rise to coexistence of stable equilibria and stable periodic solutions. These solutions may reveal some new type of patterns of complex dynamical behaviors in predator-prey systems.

AB - In this paper, we consider a predator-prey system with Holling type III ratio-dependent functional response. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. In particular, we show that the ratio-dependent predator-prey system can exhibit multiple limit cycles due to Hopf bifurcation, giving rise to coexistence of stable equilibria and stable periodic solutions. These solutions may reveal some new type of patterns of complex dynamical behaviors in predator-prey systems.

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KW - Hopf bifurcation

KW - Predator-prey system

KW - bistable, tristable

KW - focus value

KW - limit cycle

KW - normal form

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JO - International Journal of Bifurcation and Chaos

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