Experimental and numerical studies of synchronization competition in a Chua oscillator

Synchronization has become a well-known and used feature in driven chaotic oscillators. In particular, phase synchronization, has been studied in a variety of situations, both theoretical/numerical and experimental. This is the case where the amplitudes of response and drive signals are disconnected, but their phases exhibit a strong correlation. More recently, numerical and experimental studies have shown that simultaneously forcing a chaotic system with two distinct periodic oscillators yields interesting response behaviors. We present here experimental results for two different sinusoidal functions competing to phase synchronize a Chua oscillator. It shows that depending on the amplitude and frequency values of the two sinusoidal functions, the Chua oscillator can stay phase synchronized to one or the other of the inputs all the time, or can alternate synchronous states between them. We use real-time detection techniques that prove to be useful and reliable for observing synchronous and non-synchronous states, as well as transitions between them. Real-time detection capability becomes very convenient, for instance, for the adjustment of experimental control parameters to induce cases of interest. Numerical simulations confirm and validate the experimental results. One potential motivation for this work is the existence of a number of systems subject to simultaneous external influences, like two neurons sending signals to another neuron. In addition, it is a first step toward more complex experimental situations where several oscillators compete for synchronization with a single nonlinear system