scholarly journals Analysis of a predator–prey model with Holling II functional response concerning impulsive control strategy

2006 ◽  
Vol 193 (1) ◽  
pp. 347-362 ◽  
Author(s):  
Bing Liu ◽  
Zhidong Teng ◽  
Lansun Chen
Keyword(s):  
Functional Response ◽  
Control Strategy ◽  
Impulsive Control ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Impulsive Control Strategy ◽  
Holling Ii Functional Response

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.

DYNAMIC COMPLEXITIES IN A LOTKA–VOLTERRA PREDATOR–PREY MODEL CONCERNING IMPULSIVE CONTROL STRATEGY

2005 ◽  
Vol 15 (02) ◽  
pp. 517-531 ◽  
Author(s):  
BING LIU ◽  
YUJUAN ZHANG ◽  
LANSUN CHEN
Keyword(s):  
Periodic Solution ◽  
Control Strategy ◽  
Impulsive Control ◽  
Period Doubling ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Pest Eradication ◽  
Impulsive Control Strategy

Based on the classical Lotka–Volterra predator–prey system, an impulsive differential equation to model the process of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is proposed and investigated. It is proved that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Otherwise, the system can be permanent. We observe that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently. Numerical results show that the system we considered has more complex dynamics including period-doubling bifurcation, symmetry-breaking bifurcation, period-halving bifurcation, quasi-periodic oscillation, chaos and nonunique dynamics, meaning that several attractors coexist. Finally, a pest–predator stage-structured model for the pest concerning this kind of impulsive control strategy is proposed, and we also show that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some threshold.

scholarly journals Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yanzhen Wang ◽  
Min Zhao
Keyword(s):  
Functional Response ◽  
Impulsive Control ◽  
Control Strategies ◽  
Positive Periodic Solution ◽  
Pitchfork Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Prey Model ◽  
Bifurcation Chaos

The dynamic behavior of a predator-prey model with Holling type IV functional response is investigated with respect to impulsive control strategies. The model is analyzed to obtain the conditions under which the system is locally asymptotically stable and permanent. Existence of a positive periodic solution of the system and the boundedness of the system is also confirmed. Furthermore, numerical analysis is used to discover the influence of impulsive perturbations. The system is found to exhibit rich dynamics such as symmetry-breaking pitchfork bifurcation, chaos, and nonunique dynamics.

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