Fast high-quality numerical shadowing of chaotic maps using synchronization.
For a chaotic, dynamical system, a typical noisy trajectory diverges exponentially from the true trajectory with the same initial conditions. Nonetheless, the noisy trajectory, as representative of the dynamical system, may have credibility if there exists a true trajectory, corresponding to a slightly different initial condition, that stays close to the noisy trajectory for long periods of time. For finding such shadowing trajectories, a synchronization based method is presented. We call it the synchronize-and-pullback algorithm. Several numerical examples are shown illustrating the method. Finally, an application of the proposed shadowing technique for noise filtration in the context of communication is presented.
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