Stability in a Discrete Fractional Order Prey Predator System with Functional Response

2017 ◽  
Vol 7 (5) ◽  
pp. 630-633 ◽  
Author(s):  
A. George Maria Selvam ◽  
◽  
R. Janagaraj ◽  
Britto Jacob. S ◽  
◽  
...  
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Predator System

scholarly journals Numerical Analysis of a Fractional Order Discrete Prey – Predator System with Functional Response

2018 ◽  
Vol 7 (4.10) ◽  
pp. 681 ◽  
Author(s):  
A. George Maria Selvam ◽  
R. Janagaraj
Keyword(s):  
Numerical Analysis ◽  
Fixed Points ◽  
Functional Response ◽  
Fractional Order ◽  
Periodic Oscillations ◽  
Numerical Examples ◽  
Discrete Equations ◽  
Predator Interactions ◽  
The Stability ◽  
Predator System

This study presents numerical examples of Discrete Fractional Order Prey Predator interactions with Functional Response. The process of discretization is applied and the version of discrete equations is obtained. Fixed points are determined and the stability around the fixed points is analyzed. Also the theoretical analysis has been verified from the numerical simulations, which help better understanding of the proposed system. Rich dynamics of system is exhibited by Bifurcation diagram and Periodic Oscillations for suitable parameters values.  

Computational Modeling and Theoretical Analysis of Nonlinear Fractional Order Prey-Predator System

Fractals ◽  
2020 ◽  
Author(s):  
Amjad Ali ◽  
Kamal Shah ◽  
Hussam Alrabaiah ◽  
Zahir Shah ◽  
Ghaus Ur Rahman ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Computational Modeling ◽  
Fractional Order ◽  
Predator System

Dynamical Behaviors of a Fractional-Order Predator–Prey Model with Holling Type IV Functional Response and Its Discretization

2019 ◽  
Vol 20 (2) ◽  
pp. 125-136
Author(s):  
A. M. Yousef ◽  
S. Z. Rida ◽  
Y. Gh. Gouda ◽  
A. S. Zaki
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Theoretical Results

AbstractIn this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.

Prey–predator model for optimal harvesting with functional response incorporating prey refuge

2015 ◽  
Vol 09 (01) ◽  
pp. 1650014 ◽  
Author(s):  
G. S. Mahapatra ◽  
P. Santra
Keyword(s):  
Functional Response ◽  
System Parameter ◽  
Optimal Harvesting ◽  
Functional Responses ◽  
Prey Refuge ◽  
Numerical Examples ◽  
Pictorial Presentation ◽  
Constant Form ◽  
Predator Model ◽  
Predator System

This paper presents a prey–predator model considering the predator interacting with non-refuges prey by class of functional responses. Here we also consider harvesting for only non-refuges prey. We discuss the equilibria of the model, and their stability for hiding prey either in constant form or proportional to the densities of prey population. We also investigate various possibilities of bionomic equilibrium and optimal harvesting policy. Finally we present numerical examples with pictorial presentation of the various effects of the prey–predator system parameter.

A fractional-order predator–prey model with Beddington–DeAngelis functional response and time-delay

2018 ◽  
Vol 27 (2) ◽  
pp. 525-538 ◽  
Author(s):  
Rajivganthi Chinnathambi ◽  
Fathalla A. Rihan ◽  
Hebatallah J. Alsakaji
Keyword(s):  
Time Delay ◽  
Functional Response ◽  
Fractional Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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