An approach toward multi-coupled oscillators

Consideration is given to a coupled system of a binary input-output version of relaxation oscillators. If the number of the oscillators is n, the circuit dynamics is described by n -dimensional linear equations which are connected to each other by hysteresis switchings, and the switching time is given explicitly. In the case of n=2, a one-dimensional return map can be obtained explicitly. It is clarified rigorously that the system exhibits various synchronous and asynchronous phenomena which correspond to all real numbers in an interval. In the case of n=3, it is verified numerically that the system exhibits more complicated synchronous and asynchronous phenomena. The approach seems to be developed toward multi-coupled cases