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Tuning Chaos Synchronization and Anti-Synchronization for Applications in Temporal Pattern Recognition

Various forms of chaotic synchronization have been proposed as ways of implementing associative memories and/or pattern recognizers. Within this context, a single chaotic dynamical system can be adopted as an implicit model of a whole class of approximately periodic signals [De Feo, 2003]. Then, by exploiting the selective properties of the recently illustrated phenomenon of Qualitative Resonance [De Feo, 2004a, 2004b], this model can be employed within a feedback-synchronization-based pattern recognition scheme. To this end, to exploit the qualitative resonance phenomenon in concrete applications, the synchronization feedback loop must be opportunely tuned. Namely, an approximately periodic pattern must regularize or reinforce the chaotic behavior of the whole system depending on whether it belongs to the class modeled by the chaotic model or not. Despite being apparently complicated, as shown here, the tuning of the synchronization feedback loop can be operated relying on standard methods from linear periodic control theory.