BIFURCATIONS AND CHAOS CONTROL IN A DISCRETE-TIME PREDATOR-PREY SYSTEM OF LESLIE TYPE

2019 ◽  
Vol 9 (1) ◽  
pp. 31-44 ◽  
Author(s):  
S. M. Sohel Rana ◽  
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
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 The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 865
Author(s):  
Jialin Chen ◽  
Xiaqing He ◽  
Fengde Chen
Keyword(s):  
Discrete Time ◽  
Food Resource ◽  
Sufficient Conditions ◽  
Iteration Scheme ◽  
Predator Species ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Fear Effect ◽  
Prey System ◽  
Trivial Equilibrium

A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results.

scholarly journals Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhihua Chen ◽  
Qamar Din ◽  
Muhammad Rafaqat ◽  
Umer Saeed ◽  
Muhammad Bilal Ajaz
Keyword(s):  
Discrete Time ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
State Feedback Control ◽  
Time Model ◽  
Predator Prey ◽  
Selective Harvesting ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Interaction

Selective harvesting plays an important role on the dynamics of predator-prey interaction. On the other hand, the effect of predator self-limitation contributes remarkably to the stabilization of exploitative interactions. Keeping in view the selective harvesting and predator self-limitation, a discrete-time predator-prey model is discussed. Existence of fixed points and their local dynamics is explored for the proposed discrete-time model. Explicit principles of Neimark–Sacker bifurcation and period-doubling bifurcation are used for discussion related to bifurcation analysis in the discrete-time predator-prey system. The control of chaotic behavior is discussed with the help of methods related to state feedback control and parameter perturbation. At the end, some numerical examples are presented for verification and illustration of theoretical findings.

scholarly journals Cooperative hunting in a discrete predator–prey system

2020 ◽  
Vol 13 (07) ◽  
pp. 2050063
Author(s):  
Yunshyong Chow ◽  
Sophia R.-J. Jang ◽  
Hua-Ming Wang
Keyword(s):  
Growth Rate ◽  
Discrete Time ◽  
Reproductive Number ◽  
Model Parameters ◽  
Predator Population ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Cooperative Hunting ◽  
Prey System ◽  
Dependent Growth

We propose and investigate a discrete-time predator–prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson–Bailey host-parasitoid system with density dependent growth rate. A sufficient condition based on the model parameters for which both populations can coexist is derived, namely that the predator’s maximal reproductive number exceeds one. We study existence of interior steady states and their stability in certain parameter regimes. It is shown that the system behaves asymptotically similar to the model with no cooperative hunting if the degree of cooperation is small. Large cooperative hunting, however, may promote persistence of the predator for which the predator would otherwise go extinct if there were no cooperation.

Sign in / Sign up

Export Citation Format

Share Document