Design of an analog chaos-generating circuit using piecewise-constant dynamics

One of the major concerns related to the analysis of chaos in nonlinear continuous-time dynamics is the difficulty involved in demonstrating chaotic behavior in a rigorous sense, and this problem has attracted intensive research interest in the last three decades. Many researchers have attempted to solve this problem by adopting simpler dynamics. In this study, we propose an extremely simple third-order chaos-generating circuit with a diode whose governing equation is represented by a piecewise-constant dynamical system. Note that the memory elements of our circuit are capacitors only. We consider the idealized case where the diode is assumed to operate as a switch. In this case, the Poincare return map is constructed from a piecewise-linear 1D map. We analytically prove the generation of chaos with a positive Lyapunov exponent through a simple systematic procedure, and observe the attractor through laboratory measurements. We strongly believe that the explicit simplicity of the proposed circuit dynamics could significantly affect the architecture of chaos-generating circuit design in application because the procedure for proving chaos is systematic, and our circuit is expected to extend to higher-dimensional circuits in a systematic manner.