Hopf bifurcation and non-hyperbolic equilibrium in a ratio-dependent predator-prey model with linear harvesting rate: analysis and computation

DOI10.1016/j.mcm.2009.04.018zbMath1185.34047OpenAlexW2091785626WikidataQ115568933 ScholiaQ115568933MaRDI QIDQ969888

Min Xiao, Cao, Jinde

Publication date: 8 May 2010

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2009.04.018

zbMATH Keywords

periodic solutionsHopf bifurcationnon-hyperbolic equilibriumpredator-prey modelratio-dependentlinear harvesting rate

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (14)

Stability and bifurcation analysis in a predator-prey system with Michaelis-Menten type predator harvesting ⋮ Qualitative analysis of a Leslie-Gower predator-prey system with nonlinear harvesting in predator ⋮ On the nature of bifurcation in a ratio-dependent predator-prey model with delays ⋮ Dynamic behaviour of a reaction-diffusion predator-prey model with both refuge and harvesting ⋮ Hopf bifurcation for a differential-algebraic biological economic system with time delay ⋮ Diffusive induced global dynamics and bifurcation in a predator-prey system ⋮ Dynamical analysis of a Beddington-DeAngelis interacting species system with prey harvesting ⋮ Spatiotemporal dynamics of a predator-prey system with linear harvesting rate ⋮ Relationship between exploitation, oscillation, MSY and extinction ⋮ Dynamics of generalist predator in a stochastic environment: effect of delayed growth and prey refuge ⋮ Stability and global Hopf bifurcation analysis on a ratio-dependent predator-prey model with two time delays ⋮ Analysis of Bogdanov-Takens bifurcations in a spatiotemporal harvested-predator and prey system with Beddington-DeAngelis-type response function ⋮ Stability and bifurcation for a single-species model with delay weak kernel and constant rate harvesting ⋮ ANALYSIS OF BOGDANOV–TAKENS BIFURCATION OF CODIMENSION 2 IN A GAUSE-TYPE MODEL WITH CONSTANT HARVESTING OF BOTH SPECIES AND DELAY EFFECT

Cites Work

• About deterministic extinction in ratio-dependent predator-prey models
• Computing the heteroclinic bifurcation curves in predator-prey systems with ratio-dependent functional response
• Coexistence properties of some predator-prey systems under constant rate harvesting and stocking
• Singularities of vector fields on the plane
• Stability regions in predator-prey systems with constant-rate prey harvesting
• 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
• Heteroclinic bifurcation in a ratio-dependent predator-prey system
• Population models with singular equilibrium
• Bifurcations of a Ratio-Dependent Predator-Prey System with Constant Rate Harvesting
• 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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