Synchronization of Chaotic Attractors

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:
,
,
,
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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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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