scholarly journals BIFURCATION AND CHAOS IN A DISCRETE TIME PREDATOR-PREY SYSTEM OF LESLIE TYPE WITH GENERALIZED HOLLING TYPE Ⅲ FUNCTIONAL RESPONSE

2017 ◽  
Vol 7 (2) ◽  
pp. 411-426
Author(s):  
Ali Atabaigi ◽  
Keyword(s):  
Functional Response ◽  
Discrete Time ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Prey System

Complex dynamics of a discrete-time predator-prey system with Holling IV functional response

2016 ◽  
Vol 87 ◽  
pp. 158-171 ◽  
Author(s):  
Qianqian Cui ◽  
Qiang Zhang ◽  
Zhipeng Qiu ◽  
Zengyun Hu
Keyword(s):  
Functional Response ◽  
Discrete Time ◽  
Complex Dynamics ◽  
Predator Prey ◽  
Prey System

scholarly journals Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
S. M. Sohel Rana ◽  
Umme Kulsum
Keyword(s):  
Functional Response ◽  
Discrete Time ◽  
Chaos Control ◽  
Phase Portraits ◽  
Closed Cycle ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Period 2 ◽  
Maximum Lyapunov Exponents

The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of R+2. Numerical simulations are presented not only to validate analytical results but also to show chaotic behaviors which include bifurcations, phase portraits, period 2, 4, 6, 8, 10, and 20 orbits, invariant closed cycle, and attracting chaotic sets. Furthermore, we compute numerically maximum Lyapunov exponents and fractal dimension to justify the chaotic behaviors of the system. Finally, a strategy of feedback control is applied to stabilize chaos existing in the system.

scholarly journals Complex Dynamics of a Discrete-Time Predator-Prey System with Ivlev Functional Response

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Hunki Baek
Keyword(s):  
Functional Response ◽  
Discrete Time ◽  
Complex Dynamics ◽  
Discrete Systems ◽  
Flip Bifurcation ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Dynamical Complexity ◽  
Dynamical Behaviors ◽  
Prey System

The dynamics of a discrete-time predator-prey system with Ivlev functional response is investigated in this paper. The conditions of existence for flip bifurcation and Hopf bifurcation in the interior of R+2 are derived by using the center manifold theorem and bifurcation theory. Numerical simulations are presented not only to substantiate our theoretical results but also to illustrate the complex dynamical behaviors of the system such as attracting invariant circles, periodic-doubling bifurcation leading to chaos, and periodic-halving phenomena. In addition, the maximum Lyapunov exponents are numerically calculated to confirm the dynamical complexity of the system. Finally, we compare the system to discrete systems with Holling-type functional response with respect to dynamical behaviors.

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