# Synchronization Phenomena in Oscillatory Circuits Coupled by Time-Varying Resistors

In recent years, many people have been trying to develop some applications to information processing by exploiting synchronization phenomena in coupled oscillatory systems. Such oscillatory systems can produce some kinds of phase patterns, and they may be utilized modeling of associative memory and learning process. Endo et al. have reported details of theoretical analysis and circuit experiments about some coupled oscillators as a ladder, a ring and a two-dimensional array. There are systems the dissipation factors of which vary with time. Examples are the time-variation of the ambient temperature, equations describing an object moving in a space with some friction, or an equation governing a circuit with a resistor the temperature coefficient of which is sensitive, such as thermistor. As there are few discussions of this topic as yet, we investigate the synchronization phenomena in oscillatory circuits coupled by time varying resistors. We implement the time-varying resistor by switching a positive and a negative resistor periodically. This proposed oscillatory system is novel. By computer simulations, we find various interesting phenomena like wave propagation, clustering, complex phase patterns, and cellular automata-like behavior, that are not observed in simple oscillatory systems coupled by a resistor.