This paper studies a pulse-coupled network consisting of simple chaotic spiking oscillators (CSOs). If a unit oscillator and its neighbor(s) have (almost) the same parameter values, they exhibit in-phase synchronization of chaos. As the parameter values differ, they exhibit asynchronous phenomena. Based on such behavior, some synchronous groups appear partially in the network. Typical phenomena are verified in the laboratory via a simple test circuit. These phenomena can be evaluated numerically by using an effective mapping procedure. We then apply the proposed network to image segmentation. Using a lattice pulse-coupled network via grouping synchronous phenomena, the input image data can be segmented into some sub-regions.
Abstrnct -This paper discusses an approach toward higher dimensional autonomous chaotic circuits. We especially consider a particular class of circuits which includes only one nonlinear element, a three segments piecewise-linear resistor, and one small inductor La serially connected with it. The contents are divided into two parts. Part 1 gives a simple fourdimensional example that realizes hyperchaos. For the case where La is shorted, the circuit equation can be simplified into a constrained system and a two-dimensional Poincare map can be rigorously derived. This mapping and its Lyapunov exponents verify laboratory measurements of hyperchaos and related phenomena. Part 2 gives a rigorous approach to the singular perturbation theory of a N-dimensional circuit family which includes the example in Section I. We derive a canonical form equation which describes any circuit in this family. This equation can be simplified into a constrained system and a (N -2)-dimensional Poincare map can be derived. The main theorem indicates that this mapping explains the observable solutions of the canonical form very well.PART 1 A HYPERCHAOSGENERATOR
This paper discusses a circuit family including a dependent switched capacitor (DSC). The DSC function is instantaneously short of one capacitor at the moment when its voltage reaches a threshold. The chaos generation can be guaranteed theoretically, We also consider a master-slave system. If there does not exist a homoclinic orbit in the master chaos attractor, it exhibits either in-phase or inverse-phase synchronization of chaos. If there exists a homoclinic orbit, the synchronization is broken down. We explain the synchronization mechanism and evaluate its robustness theoretically. The theoretical results have been verified in laboratory experiments.
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