Chaotic Switching of Phase States in Time-Varying Coupled Circuits

Synchronization phenomena in complex systems are very interesting to describe various higher-dimensional nonlinear phenomena in the field of natural science. Studies on synchronization phenomena of coupled oscillators are extensively carried out in various fields, physics [1]-[4], biology [5], [6] engineering [7]-[11] and so on. Because many researchers suggest that synchronization phenomena of coupled oscillators have some relations to information processing in the brain. We consider that it is very important to investigate the synchronization phenomena of coupled oscillators to realize a brain computer for the future engineering application. On the other hand, there are some systems whose dissipation factors vary with time, for example, under the time-variation of the ambient temperature, an equation describing an object moving in a space with some friction and an equation governing a circuit with a resistor whose temperature coefficient is sensitive such as thermistor. However, there are few discussions about coupled oscillators coupling by a time-varying resistor. In our previous research, we have investigated synchronization phenomena in van der Pol oscillators coupled by a time-varying resistor [12]. We realized the time-varying resistor by switching a positive and a negative resistors periodically. By changing the duty ratio p, we confirmed that the characteristics of the synchronization phenomena changed as follows. First, for smaller p, the two coupled oscillators are synchronized only in antiphase. Second, for intermediate p, the coexistence of the in-phase and the anti-phase synchronizations can be observed. Finally, for larger p, only the in-phase synchronization can be confirmed. We consider what complex synchronization phenomena can be observed, when chaotic circuits are coupled by time-varying resistor. In this study, two chaotic circuits coupled by a time-varying resistor are investigated. First, the coexistence of in-phase and anti-phase synchronization are observed. Next, we confirm that interesting synchronization phenomena with switching phase states between the two chaotic circuits can be observed when the strength of coupling parameter R is decreased. Furthermore, the sojourn time of the in-phase and the anti-phase are investigated. We confirm that the sojourn time depends on the frequency and the strength of the time-varying resistor.