Bifurcations and Chaos Generation from 1D or 2D Circuits Including Switches

Abstract

Generation of chaos is of the highest interest for many kind of applications as secure transmissions, image processing or telecommunications. In order to obtain chaotic signals that can be used in applications, simple circuits including switches have been considered those last years. Their interest is of two types: first, they belong to the class of hybrid systems that have recently attracted a great interest, secondly, they permit to obtain chaos in a very easy way. Such circuits are very easy to implement and robust chaos can be obtained, depending upon parameter values. For this aim, it is necessary to study and understand the bifurcation structures of the circuit model. In this paper, we propose two kinds of chaos generators obtained from simple RC circuits including switches managed using a clock (impulse waveform) and the charging/discharging of the capacitors. Our models are given via one-dimensional (1D) or two-dimensional (2D) nonlinear maps. We present the bifurcation studies permitting to understand the evolution of the behaviour of our systems and the appearance of chaos.

Keywords

• chaotic signal
• bifurcation
• switching circuit
• piecewise-smooth map