Bifurcation of a predator–prey model with disease in the prey

Bifurcation of a predator–prey model with disease in the prey

In this paper, a predator–prey model with disease in the prey is considered. Assume that the predator eats only the infected prey, and the incidence rate is nonlinear. We study the dynamics of the model in terms of local analysis of equilibria and bifurcation analysis of a boundary equilibrium and a...

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Veröffentlicht in:Nonlinear dynamics 2010-12, Vol.62 (4), p.841-850
Hauptverfasser: Liu, Xuanliang, Wang, Chaoyang
Format: Artikel
Sprache:eng
Schlagworte:
Automotive Engineering
Bifurcation theory
Bifurcations
Boundaries
Classical Mechanics
Computer simulation
Control
Dynamic tests
Dynamical Systems
Economic models
Engineering
Hopf bifurcation
Mathematical models
Mechanical Engineering
Nonlinear dynamics
Original Paper
Predator-prey simulation
Predators
Vibration
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Beschreibung
Zusammenfassung:In this paper, a predator–prey model with disease in the prey is considered. Assume that the predator eats only the infected prey, and the incidence rate is nonlinear. We study the dynamics of the model in terms of local analysis of equilibria and bifurcation analysis of a boundary equilibrium and a positive equilibrium. We discuss the Bogdanov–Takens bifurcation near the boundary equilibrium and the Hopf bifurcation near the positive equilibrium; numerical simulation results are given to support the theoretical predictions.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-010-9766-7