Effect of Parameter Mismatch in Chaotic Circuits Coupled by a Time-Varying Resistor

Synchronization phenomena in complex systems are important 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, biology, engineering and so on [1][4]. 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 timevariation 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 oscillators coupled by a time-varying resistor. In our previous study, two chaotic circuits coupled by a time-varying resistor were investigated [5]. First, the coexistence of in-phase and anti-phase synchronization was observed. Next, we have confirmed 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 times of the in-phase and the anti-phase have been investigated. We confirmed that the sojourn time depends on the frequency and the strength of the time-varying resistor. In this study, we investigate the effect of parameter mismatch in chaotic circuits coupled by a time-varying resistor. Namely, the two chaotic circuits with different characteristics are coupled. We give the parameter mismatch of β to the two chaotic circuits. We consider that it is very important to observe the difference of synchronization phenomena between symmetric and asymmetric systems. By computer simulations, we can observe very interesting synchronization phenomenon which means that the sojourn times of in-phase and anti-phase states become longer when the parameter mismatch increases.