Neimark–Sacker bifurcation and chaos control in discrete-time predator–prey model with parasites

2018 ◽  
Vol 94 (4) ◽  
pp. 2527-2536 ◽  
Author(s):  
Umer Saeed ◽  
Irfan Ali ◽  
Qamar Din
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Discrete-time predator-prey model with flip bifurcation and chaos control

2020 ◽  
Vol 17 (5) ◽  
pp. 5944-5960
Author(s):  
A. Q. Khan ◽  
◽  
I. Ahmad ◽  
H. S. Alayachi ◽  
M. S. M. Noorani ◽  
...  
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Flip Bifurcation ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Dynamics of a Discrete-time Predator-Prey Model of Leslie type with Predator Harvesting

2021 ◽  
Vol 1850 (1) ◽  
pp. 012120
Author(s):  
S. Vinoth ◽  
R. Sivasamy ◽  
K. Sathiyanathan
Keyword(s):  
Discrete Time ◽  
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 Discrete-Time Predator-Prey Model with Bifurcations and Chaos

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
K. S. Al-Basyouni ◽  
A. Q. Khan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Discrete Time ◽  
Control Method ◽  
Linear Stability Theory ◽  
Flip Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Positive Fixed Point

In this paper, local dynamics, bifurcations and chaos control in a discrete-time predator-prey model have been explored in ℝ + 2 . It is proved that the model has a trivial fixed point for all parametric values and the unique positive fixed point under definite parametric conditions. By the existing linear stability theory, we studied the topological classifications at fixed points. It is explored that at trivial fixed point model does not undergo the flip bifurcation, but flip bifurcation occurs at the unique positive fixed point, and no other bifurcations occur at this point. Numerical simulations are performed not only to demonstrate obtained theoretical results but also to tell the complex behaviors in orbits of period-4, period-6, period-8, period-12, period-17, and period-18. We have computed the Maximum Lyapunov exponents as well as fractal dimension numerically to demonstrate the appearance of chaotic behaviors in the considered model. Further feedback control method is employed to stabilize chaos existing in the model. Finally, existence of periodic points at fixed points for the model is also explored.

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