scholarly journals Chaotic dynamics in a simple predator-prey model with discrete delay

2021 ◽  
Vol 26 (1) ◽  
pp. 191-216
Author(s):  
Guihong Fan ◽  
◽  
Gail S. K. Wolkowicz ◽  
Keyword(s):  
Chaotic Dynamics ◽  
Discrete Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

ROLE OF HARVESTING IN CONTROLLING CHAOTIC DYNAMICS IN THE PREDATOR–PREY MODEL WITH DISEASE IN THE PREDATOR

2013 ◽  
Vol 06 (02) ◽  
pp. 1350005 ◽  
Author(s):  
KRISHNA PADA DAS ◽  
SANJAY CHAUDHURI
Keyword(s):  
Chaotic Dynamics ◽  
Large Population ◽  
Model System ◽  
Predator Population ◽  
Predator Prey ◽  
Force Of Infection ◽  
Predator Prey Model ◽  
Prey Model ◽  
Reproduction Numbers

Predator–prey model with harvesting is well studied. The role of disease in such system has a great importance and cannot be ignored. In this study we have considered a predator–prey model with disease circulating in the predator population only and we have also considered harvesting in the prey and in the susceptible predator. We have studied the local stability, Hopf bifurcation of the model system around the equilibria. We have derived the ecological and the disease basic reproduction numbers and we have observed its importance in the community structure of the model system and in controlling disease propagation in the predator population. We have paid attention to chaotic dynamics for increasing the force of infection in the predator. Chaotic population dynamics can exhibit irregular fluctuations and violent oscillations with extremely small or large population abundances. In this study main objective is to show the role of harvesting in controlling chaotic dynamics. It is observed that reasonable harvesting on the prey and the susceptible predator prevents chaotic dynamics.

A RATIO-DEPENDENT PREDATOR-PREY MODEL WITH DELAY AND HARVESTING

2010 ◽  
Vol 18 (02) ◽  
pp. 437-453 ◽  
Author(s):  
A. K. MISRA ◽  
B. DUBEY
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Functional Response ◽  
Bifurcation Parameter ◽  
Discrete Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

In this paper a predator-prey model with discrete delay and harvesting of predator is proposed and analyzed by considering ratio-dependent functional response. Conditions of existence of various equilibria and their stability have been discussed. By taking delay as a bifurcation parameter, the system is found to undergo a Hopf bifurcation. Numerical simulations are also performed to illustrate the results.

DYNAMICS OF A STAGE-STRUCTURED PREDATOR-PREY MODEL CONCERNING IMPULSIVE CONTROL STRATEGY

2009 ◽  
Vol 17 (04) ◽  
pp. 779-792 ◽  
Author(s):  
YANKE DU ◽  
RUI XU ◽  
LIJIANG DUAN
Keyword(s):  
Control Strategy ◽  
Chaotic Dynamics ◽  
Complex Dynamics ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Characteristic Sequence ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Impulsive Control Strategy

A stage-structured predator-prey model concerning impulsive control strategy is proposed and investigated. The global attractiveness of the pest-eradication periodic solution is discussed, and sufficient conditions are obtained for the permanence of the system. Further, numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.

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