Transforming subharmonic chaos to homoclinic chaos suitable for pattern recognition

Various forms of chaotic synchronization have been proposed as ways of realizing associative memories and/or pattern recognizers. To exploit this kind of synchronization phenomena in temporal pattern recognition, a chaotic dynamical system representing the class of signals that are to be recognized must be established. As shown recently [De Feo, 2003], this system can be determined by means of identification techniques where chaos emerges by itself to model the diversity of nearly periodic signals. However, the emerging chaotic behavior is subharmonic, i.e. period doubling-like, and therefore, as explained in [De Feo, 2004a, 2004b], it is not suitable for a synchronization-based pattern recognition technique. Nevertheless, as shown here, bifurcation theory and continuation techniques can be combined to modify a subharmonic chaotic system and drive it to homoclinic conditions; obtaining in this way a model suitable for synchronization-based pattern recognition.