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 e valuated. Owing to the piecewise-linear nature of the nonlinear elements of the circuit, such bifurcations are discussed by resorting to a suitable on e-dimensional map. As the ordinary differential equations governing the cir cuit are piecewise linear, the analytical expressions of their solutions ca n be derived in each linear region. Consequently, the proposed results have been obtained not by resorting to numerical integration, but by properly c onnecting pieces of planar flows. The bifurcation analysis is carried out b y varying one of the three dimensionless parameters that the system of norm alized 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 dyna mics.