scholarly journals A Predator-Prey Model with Functional Response and Stage Structure for Prey

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Xiao-Ke Sun ◽  
Hai-Feng Huo ◽  
Xiao-Bing Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Stage Structure ◽  
Transcendental Equation ◽  
Positive Equilibrium ◽  
Type Ii ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Type Ii Functional Response

A predator-prey system with Holling type II functional response and stage structure for prey is presented. The local and global stability are studied by analyzing the associated characteristic transcendental equation and using comparison theorem. The existence of a Hopf bifurcation at the positive equilibrium is also studied. Some numerical simulations are also given to illustrate our results.

scholarly journals Hopf bifurcation analysis in a stage-structure predator–prey model with two time delay

2022 ◽  
Vol 355 ◽  
pp. 03048
Author(s):  
Bochen Han ◽  
Shengming Yang ◽  
Guangping Zeng
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Local Stability ◽  
Time Delays ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Predator Model

In this paper, we consider a predator-prey system with two time delays, which describes a prey–predator model with parental care for predators. The local stability of the positive equilibrium is analysed. By choosing the two time delays as the bifurcation parameter, the existence of Hopf bifurcation is studied. Numerical simulations show the positive equilibrium loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold.

scholarly journals Global dynamics of a predator-prey system with Holling type II functional response

2011 ◽  
Vol 16 (2) ◽  
pp. 242-253 ◽  
Author(s):  
Xiaohong Tian ◽  
Rui Xu
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Global Dynamics ◽  
Type Ii ◽  
Asymptotically Stable ◽  
Predator Prey ◽  
Prey System ◽  
Coexistence Equilibrium ◽  
Type Ii Functional Response

In this paper, a predator-prey system with Holling type II functional response and stage structure is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is studied. The existence of the orbitally asymptotically stable periodic solution is established. By using suitable Lyapunov functions and the LaSalle invariance principle, it is proven that the predator-extinction equilibrium is globally asymptotically stable when the coexistence equilibrium is not feasible, and sufficient conditions are derived for the global stability of the coexistence equilibrium.

scholarly journals Long-Time Behaviours of a Stochastic Predator-Prey System with Holling-Type II Functional Response and Regime Switching

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Weili Kong ◽  
Yuanfu Shao
Keyword(s):  
White Noise ◽  
Functional Response ◽  
Regime Switching ◽  
Type Ii ◽  
Stochastic Permanence ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Long Time ◽  
Type Ii Functional Response

Considering the impacts of white noise, Holling-type II functional response, and regime switching, we formulate a stochastic predator-prey model in this paper. By constructing some suitable functionals, we establish the sufficient criteria of the stationary distribution and stochastic permanence. By numerical simulations, we illustrate the results and analyze the influence of regime switching on the dynamics.

scholarly journals Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Can-Yun Huang ◽  
Min Zhao ◽  
Hai-Feng Huo
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Ii Functional Response

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.

scholarly journals The Dynamical Behavior of a Predator-Prey System with Holling Type II Functional Response and Allee Effect

2020 ◽  
Vol 11 (05) ◽  
pp. 407-425
Author(s):  
Shuangte Wang ◽  
Hengguo Yu ◽  
Chuanjun Dai ◽  
Min Zhao
Keyword(s):  
Functional Response ◽  
Allee Effect ◽  
Dynamical Behavior ◽  
Type Ii ◽  
Predator Prey ◽  
Prey System ◽  
Type Ii Functional Response
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