Heteroclinic bifurcation in memristor oscillators

A simple memristor-based oscillatory network has been recently proposed as building block for the realization of associative and dynamic oscillatory memories for spatio-temporal pattern recognition applications. The network was found to experience a gamut of complex dynamic behaviors. A complete picture of the network dynamics requires a preliminary study of the basic oscillator. Study of its local behavior shows how a Hopf bifurcation gives rise to autonomous oscillations. Sweep of a control parameter causes such oscillations to grow and suddenly disappear through a global Heteroclinic bifurcation. Since the occurrence of such global event in the oscillatory memory would impair its performance, this work presents a detailed mathematical analysis of the Heteroclinic bifurcation and derives necessary and sufficient conditions for its avoidance.