Global Bifurcation for a Predator-Prey Model with Ivlev Functional Response

2010 ◽  
Author(s):  
Shuling Zha ◽  
Gaihui Guo
Keyword(s):  
Functional Response ◽  
Global Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

BIFURCATION AND CHAOS IN A DISCRETE PREDATOR–PREY MODEL WITH HOLLING TYPE-III FUNCTIONAL RESPONSE AND HARVESTING EFFECT

2021 ◽  
pp. 1-28
Author(s):  
ANURAJ SINGH ◽  
PREETI DEOLIA
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Flip Bifurcation ◽  
Bifurcation Structure ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey Model ◽  
Wide Range

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting.

scholarly journals Dynamical behavior of a stochastic predator-prey model with general functional response and nonlinear jump-diffusion

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xinhong Zhang ◽  
Qing Yang
Keyword(s):  
Functional Response ◽  
Dynamical Behavior ◽  
Uniform Boundedness ◽  
Jump Diffusion ◽  
Necessary Condition ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
A New Technique ◽  
The One

<p style='text-indent:20px;'>In this paper, we consider a stochastic predator-prey model with general functional response, which is perturbed by nonlinear Lévy jumps. Firstly, We show that this model has a unique global positive solution with uniform boundedness of <inline-formula><tex-math id="M1">\begin{document}$ \theta\in(0,1] $\end{document}</tex-math></inline-formula>-th moment. Secondly, we obtain the threshold for extinction and exponential ergodicity of the one-dimensional Logistic system with nonlinear perturbations. Then based on the results of Logistic system, we introduce a new technique to study the ergodic stationary distribution for the stochastic predator-prey model with general functional response and nonlinear jump-diffusion, and derive the sufficient and almost necessary condition for extinction and ergodicity.</p>

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