Bifurcation analysis of a PWL chaotic circuit based on hysteresis through a one-dimensional map

Bifurcations in the dynamics of a chaotic circuit based on hysteresis are evaluated. Owing to the piecewise-linear nature of the nonlinear elements of the circuit, such bifurcations are discussed by resorting to a suitable one-dimensional map. As the ordinary differential equations governing the circuit are piecewise linear, the analytical expressions of their solutions can be derived in each linear region. Consequently, the proposed results have been obtained not by resorting to numerical integration, but by properly connecting pieces of planar flows. The bifurcation analysis is carried out by varying one of the three dimensionless parameters that the system of normalized circuit equations depends on. Local and global bifurcations, regular and chaotic asymptotic behaviors are pointed out by analyzing both the one-dimensional map and the three-dimensional flow induced by the circuit dynamics.