scholarly journals Multiple Bifurcations in a Delayed Predator–Prey System with Nonmonotonic Functional Response

2001 ◽  
Vol 176 (2) ◽  
pp. 494-510 ◽  
Author(s):  
Dongmei Xiao ◽  
Shigui Ruan
Keyword(s):  
Functional Response ◽  
Predator Prey ◽  
Prey System ◽  
Nonmonotonic Functional Response

Bifurcation analysis of a diffusive predator–prey system with nonmonotonic functional response

2018 ◽  
Vol 94 (4) ◽  
pp. 2901-2918
Author(s):  
Bounsanong Sounvoravong ◽  
Jianping Gao ◽  
Shangjiang Guo
Keyword(s):  
Functional Response ◽  
Bifurcation Analysis ◽  
Predator Prey ◽  
Prey System ◽  
Nonmonotonic Functional Response

THE EFFECT OF DIFFUSION FOR A PREDATOR–PREY SYSTEM WITH NONMONOTONIC FUNCTIONAL RESPONSE

2004 ◽  
Vol 14 (12) ◽  
pp. 4309-4316 ◽  
Author(s):  
ZHIHUA LIU ◽  
RONG YUAN
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Functional Response ◽  
Bifurcation Analysis ◽  
Predator Prey ◽  
Prey System ◽  
Nonmonotonic Functional Response

We consider the delayed predator–prey system with diffusion. The bifurcation analysis of the model shows that Hopf bifurcation can occur under some conditions and the system has a Bogdanov–Takens singularity for any time delay value.

scholarly journals Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
Xuepeng Li ◽  
Wensheng Yang
Keyword(s):  
Time Delay ◽  
Functional Response ◽  
Negative Feedback ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Prey Population ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent ◽  
Nonmonotonic Functional Response

Sufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay    are obtained, where and stand for the density of the prey and the predator, respectively, and is a constant. stands for the time delays due to negative feedback of the prey population.

scholarly journals Bifurcation Analysis of a Predator-Prey System with Nonmonotonic Functional Response

2003 ◽  
Vol 63 (2) ◽  
pp. 636-682 ◽  
Author(s):  
Huaiping Zhu ◽  
Sue Ann Campbell ◽  
Gail S. K. Wolkowicz
Keyword(s):  
Functional Response ◽  
Bifurcation Analysis ◽  
Predator Prey ◽  
Prey System ◽  
Nonmonotonic Functional Response

scholarly journals Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xiaozhou Feng ◽  
Hao Sun ◽  
Yangfan Xiao ◽  
Feng Xiao
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Upper And Lower Bounds ◽  
Positive Equilibrium ◽  
Equilibrium Solutions ◽  
Predator Prey ◽  
Fear Effect ◽  
Prey System ◽  
Nonmonotonic Functional Response

This paper investigates the diffusive predator-prey system with nonmonotonic functional response and fear effect. Firstly, we discussed the stability of the equilibrium solution for a corresponding ODE system. Secondly, we established a priori positive upper and lower bounds for the positive solutions of the PDE system. Thirdly, sufficient conditions for the local asymptotical stability of two positive equilibrium solutions of the system are given by using the method of eigenvalue spectrum analysis of linearization operator. Finally, the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system are established by the Leray–Schauder degree theory and Poincaré inequality.

Higher Codimension Bifurcation Analysis of Predator–Prey Systems with Nonmonotonic Functional Responses

2020 ◽  
Vol 30 (12) ◽  
pp. 2050167
Author(s):  
Jinhui Yao ◽  
Guihua Li ◽  
Gang Guo
Keyword(s):  
Functional Response ◽  
Positive Equilibrium ◽  
Cusp Point ◽  
Functional Responses ◽  
Predator Prey ◽  
Prey System ◽  
Saddle Node ◽  
Boundary Equilibrium ◽  
Nonmonotonic Functional Response ◽  
Nilpotent Saddle

In this paper, we study the dynamic behaviors of a predator–prey system with a general form of nonmonotonic functional response. Through analysis, it is found that the system exists in extinction equilibrium, boundary equilibrium and two positive equilibria, one or no positive equilibrium. Furthermore, the conditions are given such that the boundary equilibrium is a saddle, node or a saddle-node point of codimension 1, 2 or 3. Then, some conditions are obtained so that the unique positive equilibrium of the system is a cusp point of codimension 2, 3 and higher or a saddle-node one of codimension 1 or 3, or a nilpotent saddle-node of codimension 4. When there are two positive equilibria in the system, the equilibrium with a large number of preys is a saddle point. For the other one, the system may undergo Hopf bifurcation. To verify our conclusion, we consider the functional response function in the literature [ Zhu et al., 2002 ; Xiao & Ruan, 2001 ]. Finally, we give a brief discussion and numerical simulation.

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