Local Activity Principle in Memristor based Simple Oscillator

This paper presents that a nonlinear system may undergo oscillating phenomenon if and only if, it satisfies the principle of local activity. With the examples of serial configuration of positive-temperature coefficient (PTC) memristor and inductor, and PTC memristor and negative-temperature coefficient (NTC) memristor, this manuscript provides a rigorous proof that at least one component must be locally active for the emergent of complex phenomena such as oscillation in the system. It is demonstrated that, the external stimulus parameter such as voltage selected in a specific subset of the locally active and the unstable regime induce oscillations in the nonlinear systems. This study significantly offers a potential application of such oscillator in various research fields for the modeling of biological neurons, signal processing and designing of complicated electronic oscillators in the context of nonlinear dynamics.