Large deviations for the stochastic predator–prey model with nonlinear functional response

2017 ◽  
Vol 54 (2) ◽  
pp. 507-521 ◽  
Author(s):  
M. Suvinthra ◽  
K. Balachandran
Keyword(s):  
Weak Convergence ◽  
Large Deviations ◽  
Functional Response ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Solution Processes ◽  
Prey Model

AbstractIn this paper we consider a diffusive stochastic predator–prey model with a nonlinear functional response and the randomness is assumed to be of Gaussian nature. A large deviation principle is established for solution processes of the considered model by implementing the weak convergence technique.

scholarly journals Dynamics of a Diffusive Predator-Prey Model with General Nonlinear Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Parameter Configuration ◽  
Sufficient And Necessary Conditions ◽  
Steady State Solutions

We study a diffusive predator-prey model with nonconstant death rate and general nonlinear functional response. Firstly, stability analysis of the equilibrium for reduced ODE system is discussed. Secondly, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. Furthermore, sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of Lyapunov function. Finally, we show that there are no nontrivial steady state solutions for certain parameter configuration.

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.

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