Pulse-coupled networks of chaotic oscillators ; analysis of rich synchronous phenomena and consideration of classification functions

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We have analyzed rich nonlinear phenomena in pulse-train generators (PGCs), PCGs with pulse-train inputs and pulse-coupled networks (PCNs) of the PCGs. We have also considered bases of engineering applications of the PCNs. The results are represented by the following:1.We have presented a simple example of the PGC consisting of an RLC circuit and a firing switch. Using a mapping procedure we have analyzed the circuit theoretically : for R<0 we have given parameters conditions for chaos generation ; and for R>0 we have given parameters condition for generation of equilibrium attractor, periodic attractor and co-existence of them.2.We have constructed an analysis method of PGCs with pulse-train inputs. We then have shown that, basically, the PGCs can synchronize with the input if the input frequency is close to multiple of some basic frequency. Rich bifurcation phenomena occur near boundary between synchronous and asynchronous phases. For R>0, we have discovered that the periodic input can change an equilibrium attractor into chaotic one. It corresponds to a novel simple nonautonomous chaotic circuit.3.We have constructed a PCN of two chaotic PGCs and have analyzed the synchronous phenomena; As parameter values of the PGCs are close to each other the PCN exhibits chaos synchronization. As the parameters vary the synchronization is to be broken down. The synchronization characteristics depend heavily on the refractory threshold and are evaluated quantitatively.4.We have constructed a mesh-type PCN of chaotic PGCs and have discovered chaotic local synchonization phenomena : chaotic PCGs having similar parameter values form a group by mutual synchronization and each group is identified by asynchronization between different groups. In order to apply the chaotic local synchronization to image segmentation, some basic numerical experiments have been performed. A simple implementation method is also presented : the implementation uses capacitors, VCCSs and analog switches.