scholarly journals Numerical Investigation of Fuzzy Predator-Prey Model with a Functional Response of the Form Arctan(ax)

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1919
Author(s):  
Saed Mallak ◽  
Doa’a Farekh ◽  
Basem Attili
Keyword(s):  
Numerical Simulation ◽  
Numerical Investigation ◽  
Functional Response ◽  
Kutta Method ◽  
Predator Prey ◽  
Generalized Hukuhara Derivative ◽  
Predator Prey Model ◽  
Runge Kutta Method ◽  
Prey Model ◽  
Over Time

In this paper we study a fuzzy predator-prey model with functional response arctan(ax). The fuzzy derivatives are approximated using the generalized Hukuhara derivative. To execute the numerical simulation, we use the fuzzy Runge-Kutta method. The results obtained over time for the evolution and the population are presented numerically and graphically with some conclusions.

The coexistence states for a predator-prey model with holling-type IV functional response

2019 ◽  
Author(s):  
Pan Xue ◽  
Cuiping Ren ◽  
Hailong Yuan
Keyword(s):  
Functional Response ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Prey Model ◽  
Coexistence States

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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