Computing the heteroclinic bifurcation curves in predator-prey systems with ratio-dependent functional response

DOI10.1007/s00285-007-0153-zzbMath1160.34048OpenAlexW2007274235WikidataQ51896868 ScholiaQ51896868MaRDI QIDQ938192

Shigui Ruan, Yilei Tang, Wei Nian Zhang

Publication date: 18 August 2008

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00285-007-0153-z

zbMATH Keywords

heteroclinic orbitMelnikov functionHamiltonian systempredator-prey systemheteroclinic bifurcationBetafunction

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Qualitative investigation and simulation of ordinary differential equation models (34C60) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

Global Stability and Canard Explosions of the Predator-Prey Model with the Sigmoid Functional Response ⋮ Spatiotemporal dynamics in a ratio-dependent predator-prey model with time delay near the Turing-Hopf bifurcation point ⋮ Dynamics of a predator-prey system with a mate-finding Allee effect ⋮ Hopf bifurcation and non-hyperbolic equilibrium in a ratio-dependent predator-prey model with linear harvesting rate: analysis and computation ⋮ Versal unfoldings of predator-prey systems with ratio-dependent functional response ⋮ Global dynamics of a predator-prey system with density-dependent mortality and ratio-dependent functional response ⋮ Spatiotemporal Dynamics of a Diffusive Leslie–Gower Predator–Prey Model with Ratio-Dependent Functional Response ⋮ Time-delayed and stochastic effects in a predator–prey model with ratio dependence and Holling type III functional response ⋮ A general class of predation models with multiplicative Allee effect

Uses Software

• XPPAUT

Cites Work

• Unnamed Item
• Melnikov method for homoclinic bifurcation in nonlinear impact oscillators
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• High order Melnikov functions and the problem of uniformity in global bifurcation
• Global qualitative analysis of a ratio-dependent predator-prey system
• Global dynamics of a ratio-dependent predator-prey system
• Parametric analysis of the ratio-dependent predator-prey model
• A note on a result of G. S. Petrov about the weakened 16th Hilbert problem
• Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect
• Heteroclinic bifurcation in a ratio-dependent predator-prey system
• Simulating, Analyzing, and Animating Dynamical Systems
• Melnikov's method and averaging
• Heteroclinic Bifurcation in the Michaelis–Menten-Type Ratio-Dependent Predator-Prey System
• Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system

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