Synchronization of Chaotic Attractors

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This Demonstration illustrates a method for synchronizing the trajectories of two modified Lotka–Volterra systems. Synchronization is accomplished by linear feedback [1], with the governing equations of the first system [2] as follows:

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, , ,

where represents prey; and represent two different predators; and , and are positive constants. This generalized Lotka–Volterra equation is augmented by a coupled subsystem

, , .

Here, represents prey; and are predators; and , and are coupling parameters. We take with initial conditions and . When the system is uncoupled (i.e., the coupling parameters are zero), these two systems diverge rapidly; in contrast, when the system is synchronized, the trajectories become superimposed.

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Contributed by: Clay Gruesbeck (August 2013)
Open content licensed under CC BY-NC-SA


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References

[1] T. Kapitaniak, Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics, San Diego: Academic Press, 1996.

[2] J. S. Costello, "Synchronization of Chaos in a Generalized Lotka–Volterra Attractor," The Nonlinear Journal, 1, 1999 pp. 11–17.



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