Control and synchronization in nonlinear circuits by using a thermistor

Abstract

The survival and occurrence of chaos are much dependent on the intrinsic nonlinearity and parameters region for deterministic nonlinear systems, which are often represented by ordinary differential equations and maps. When nonlinear circuits are mapped into dimensional dynamical systems for further nonlinear analysis, the physical parameters of electric components, e.g. capacitor, inductor, resistance, memristor, can also be replaced by dynamical parameters for possible adjustment. Slight change for some bifurcation parameters can induce distinct mode transition and dynamics change in the chaotic systems only when the parameter is adjustable and controllable. In this paper, a thermistor is included into the chaotic Chua circuit and the temperature effect is considered by investigating the mode transition in oscillation and the dependence of Hamilton energy on parameters setting in thermistor. Furthermore, the temperature of thermistor is adjusted for finding possible synchronization between two chaotic Chua circuits connected by a thermistor. When the coupling channel via thermistor connection is activated, two identical Chua circuits (periodical or chaotic oscillation) can reach complete synchronization. In particular, two periodical Chua circuits can be coupled to present chaotic synchronization by taming parameters in thermistor of coupling channel. However, phase synchronization is reached while complete synchronization becomes difficult when the coupling channel is activated to coupling a periodical Chua circuit and a chaotic Chua circuit. It can give guidance for further control of firing behaviors in neural circuits when the thermistor can capture the heat effectively.