SYNCHRONIZATION PHENOMENA IN OSCILLATORS COUPLED BY ONE RESISTOR

There have been many investigations of mutual synchronization of oscillators. In this article, N oscillators with the same natural frequencies mutually coupled by one resistor are analyzed. In this system, various synchronization phenomena can be observed because the system tends to minimize the current through the coupling resistor. When the nonlinear characteristics are third-power, we can observe N-phase oscillation, and this system can take (N - 1)! phase states. When the nonlinear characteristics are fifth-power, we can observe (N - 1),(N - 2) ...3 and 2-phase oscillations as well as N-phase oscillations and we can get much more phase states from this system than that of the system with third-power nonlinear characteristics. Because of their coupling structure and huge number of steady states of the system, our system would be a structural element of cellular neural networks. In this study, it is confirmed that our systems can stably take huge number of phase states by theoretical analysis, computer calculations and circuit experiments.