Bifurcation and Stability Analysis of a Diffusive Predator-Prey Model with Ratio-Dependent Type III Functional Response

2017 ◽  
Vol 6 (3) ◽  
pp. 393-407
Author(s):  
M. Sivakumar ◽  
K. Balachandran
Keyword(s):  
Stability Analysis ◽  
Functional Response ◽  
Predator Prey ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent ◽  
Bifurcation And Stability ◽  
Dependent Type

A delayed ratio-dependent predator–prey model of interacting populations with Holling type III functional response

2013 ◽  
Vol 76 (1) ◽  
pp. 201-220 ◽  
Author(s):  
Pallav Jyoti Pal ◽  
Prashanta Kumar Mandal ◽  
Kaushik Kumar Lahiri
Keyword(s):  
Functional Response ◽  
Predator Prey ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey Model ◽  
Interacting Populations ◽  
Ratio Dependent

Bifurcation analysis and control of a delayed stage-structured predator–prey model with ratio-dependent Holling type III functional response

2019 ◽  
Vol 26 (13-14) ◽  
pp. 1232-1245
Author(s):  
Miao Peng ◽  
Zhengdi Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Control Method ◽  
Equilibrium Points ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

A delayed stage-structured predator–prey model with ratio-dependent Holling type III functional response is proposed and explored in this study. We discuss the positivity and the existence of equilibrium points. By choosing time delay as the bifurcation parameter and analyzing the relevant characteristic equations, the local stability of the trivial equilibrium, the predator-extinction equilibrium, and the coexistence equilibrium of the system is investigated. In accordance with the normal form method and center manifold theorem, the property analysis of Hopf bifurcation of the system is obtained. Furthermore, for the purpose of protecting the stability of such a biological system, a hybrid control method is presented to control the Hopf bifurcation. Finally, numerical examples are given to verify the theoretical findings.

Extinction and Permanence Analysis of Stochastic Predator-Prey Model with Disease, Ratio-Dependent Type Functional Response and Nonlinear Incidence Rate

2021 ◽  
Author(s):  
Conghui Xu ◽  
Yongguang Yu ◽  
Guojian Ren ◽  
Xudong Hai ◽  
Zhenzhen Lu
Keyword(s):  
Incidence Rate ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Nonlinear Incidence Rate ◽  
Predator Prey ◽  
Nonlinear Incidence ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent ◽  
Dependent Type

Abstract This paper is aimed to investigate a stochastic predator-prey model with disease in both species, which is also considered with ratio-dependent type functional response and nonlinear incidence rate. First, the existence and uniqueness of positive solution is discussed. Then, some sufficient conditions are established to ensure the solution is stochastically ultimate boundedness and permanent. Also, the extinction of susceptible prey, infected prey, susceptible predator and infected predator are analysed, respectively. Furthermore, the boundedness of moments and upper-growth rate estimation are investigated. Finally, numerical simulations are given to illustrate our main results.

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