On basic piecewise-constant systems

This paper considers basic dynamics of piecewise constant systems (PWCs). The vector field is piecewise constant and the trajectories are piecewise-linear, hence the system is well suited for both the circuit implementation and the theoretical analysis. As a typical example, we propose a simple 3-D PWC chaotic circuit consisting of three capacitors, three nonlinear voltage-controlled current sources and one ideal diode. We can analyze the circuit dynamics almost completely. Also we introduce a simple chaos synchronization method based on the sliding dynamics. Typical behaviors are demonstrated in the laboratory