Spatio-temporal chaos in simple coupled chaotic circuits

Abstract

In this paper, simple autonomous chaotic circuits coupled by resistors are investigated. By carrying out computer calculations and circuit experiments, irregular self-switching phenomenon of three spatial patterns characterized by the phase states of quasi-synchronization of chaos can be observed from only four simple chaotic circuits. This is the same phenomenon as chaotic wandering of spatial patterns observed very often from systems with a large number of degrees of freedom. Namely, one of spatial-temporal chaos observed from systems of large size can be also generated in the proposed system consisting of only four chaotic circuits. A six subcircuits case and a coupled chaotic circuits networks are also studied, and such systems are confirmed to produce more complicated spatio-temporal phenomena.

Spatio-temporal Pattern Dynamics on Stochastic Models using Coupled Chaotic Maps by Changing Coupling Strength

“…It can be considered easily that coupled chaotic systems have wide variety of phase patterns and spatio-temporal phenomena. The term "spatio-temporal" is extensively used for irregular dynamical behavior observed from large scale complex systems of the relevant to both time and space [12]. In particular, it is often observed such phenomena in large scale coupled systems or complex systems.…”

Relations between spatio-temporal phenomena and eigenvalues in mutually coupled CNNs

“…The necessary condition is described by (6), which is directly derived from those conditions obtained Turing patterns in array of coupled circuits [7]. Figure 1 shows a simulation example for pattern formation, which is carried out under a two-layer CNN array consisted of 100 × 100 cells with zero-flux boundary condition and the following parameter set: a 1 = 2.6, a 2 = 2.6,…”

“…A lot of studies on phase relationship of coupled oscillators or chaotic circuits have been widely carried out [6] [9]. One of interesting spatio-temporal phenomena -phase inversion wave has been observed in van der Pol oscillators coupled by inductors as a ladder [9].…”

“…From the middle of the last decade, the investigations about the spatiotemporal dynamics in CNNs have been widely carried out, and many papers have been published, where they have discussed pattern formations and various types of autowaves such as excitability waves, concentration waves and so on. Up to the present, these CNN arrays, which are composed of chaotic oscillators [1]- [6], second order nonlinear circuit obtained by the suitably "reducing" Chua's circuit [7], and etc. have been mainly considered.…”

“…Studies of dynamic phenomena in arrays composed of chaotic [1]- [6] and oscillatory [7]- [9] elements are very important for understanding various phenomena observed in natural fields such as biology, physics, chemistry, etc. From the middle of the last decade, the investigations about the spatiotemporal dynamics in CNNs have been widely carried out, and many papers have been published, where they have discussed pattern formations and various types of autowaves such as excitability waves, concentration waves and so on.…”