Hopf bifurcation for a predator-prey biological economic system with Holling type II functional response

DOI10.1016/j.jfranklin.2011.04.019zbMath1225.34055OpenAlexW2041091952WikidataQ115570749 ScholiaQ115570749MaRDI QIDQ553564

Jianyong Qiao, Sumit K. Garg

Publication date: 27 July 2011

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2011.04.019

zbMATH Keywords

stabilityHopf bifurcationdifferential-algebraic equations

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Ecology (92D40) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (20)

Dynamics of a predator-prey ecological system with nonlinear harvesting rate ⋮ Stability and Hopf bifurcation of a predator-prey biological economic system with nonlinear harvesting rate ⋮ Periodic solution for a stochastic non-autonomous predator-prey model with Holling II functional response ⋮ Bifurcation with regard to combined interaction parameter in a life energy system dynamic model of two components with multiple delays ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Stability and Hopf bifurcation of the coexistence equilibrium for a differential-algebraic biological economic system with predator harvesting ⋮ Bifurcation analysis of a singular bioeconomic model with allee effect and two time delays ⋮ Dynamical analysis in a hybrid bioeconomic system with multiple time delays and strong Allee effect ⋮ Bifurcation and Control in a Singular Phytoplankton-Zooplankton-Fish Model with Nonlinear Fish Harvesting and Taxation ⋮ Modeling and analysis in a prey-predator system with commercial harvesting and double time delays ⋮ Analysis of a stochastic Holling type II predator-prey model under regime switching ⋮ Complex dynamics and stability analysis in a discrete hybrid bioeconomic system with double time delays ⋮ A bioeconomic differential algebraic predator-prey model with nonlinear prey harvesting ⋮ Effects of additional food on the dynamics of a three species food chain model incorporating refuge and harvesting ⋮ Bifurcation analysis of a singular nutrient-plankton-fish model with taxation, protected zone and multiple delays ⋮ Dynamic analysis of fractional-order predator-prey biological economic system with Holling type II functional response ⋮ Hopf analysis of a differential-algebraic predator–prey model with Allee effect and time delay ⋮ Bifurcation analysis in a singular Beddington-DeAngelis predator-prey model with two delays and nonlinear predator harvesting ⋮ Modelling and analysis of a multiple delayed exploited ecosystem towards coexistence perspective

Uses Software

• Matlab

Cites Work

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• Bifurcations of a class of singular biological economic models
• Bifurcation analysis and control of a discrete harvested prey-predator system with Beddington-DeAngelis functional response
• Bifurcation analysis in a predator-prey system with stage-structure and harvesting
• Differential equations and their applications. An introduction to applied mathematics. 3rd ed
• Dynamics in a ratio-dependent predator--prey model with predator harvesting
• Dynamical behavior in a harvested differential-algebraic prey-predator model with discrete time delay and stage structure
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Hopf bifurcation and stability analysis in a harvested one-predator-two-prey model
• Locating the equilibrium points of a predator-prey model by means of affine state feedback
• Global dynamics and controllability of a harvested prey-predator system with Holling type III functional response
• Stability of a general predator-prey model

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