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Control of Hopf bifurcation and chaos in a delayed Lotka-Volterra predator-prey system with time-delayed feedbacks. (English) Zbl 1470.34192

Summary: A delayed Lotka-Volterra predator-prey system with time delayed feedback is studied by using the theory of functional differential equation and Hassard’s method. By choosing appropriate control parameter, we investigate the existence of Hopf bifurcation. An explicit algorithm is given to determine the directions and stabilities of the bifurcating periodic solutions. We find that these control laws can be applied to control Hopf bifurcation and chaotic attractor. Finally, some numerical simulations are given to illustrate the effectiveness of the results found.

MSC:

34K18 Bifurcation theory of functional-differential equations
34K35 Control problems for functional-differential equations
34K20 Stability theory of functional-differential equations
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