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Scalar feedback control in a chaotic discrete prey predator system is investigated. The existence of the fixed points and the local stability of the positive fixed point are discussed. By using center manifold theorem, it is proved rigorously that the system undergoes the flip bifurcation near the unique positive fixed point. To eliminate the undesirable chaos induced by the flip bifurcation and stabilize...
In present paper, the time-delayed feedback is coupled with a ratio-dependent predator-prey model of Holling □ type. This predator-prey system can be seen as a human-controlled biological system. Regarding the delay as parameter, we investigate the existence of local Hopf bifurcations. By using the Hassard method and the center manifold argument, we derive the explicit formulas determining the stability,...
A stage-structured predator-prey model with impulses is proposed and investigated. According to the fact of biological resource management, it is assumed that the immature individuals and the mature individuals of the predator population are divided by fixed age and that immature predator population does not have the ability to attack prey. Sufficient conditions, which guarantee the global attractivity...
A mathematical model for dynamics of a prey dependent consumption model concerning impulsive control strategy is proposed and analyzed. By using Floquet theorem and comparison theorem of impulsive differential equation, we show that there exists a globally stable pest-eradication periodic solutions when the impulsive periodic is less than some critical values. Further, the conditions for the permanence...
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