Bifurcations of nonlinear circuits with mixed mode and chaotic oscillations

Two special nonlinear circuits, each with a cubic nonlinearity, controlled element, constant source and R, L, C components, are considered in this paper. The circuits can operate in various oscillating conditions (mixed-mode, quasi-periodic and chaotic). The circuits can be considered as a coupling of two oscillators (linear and nonlinear ones). Although simple topologically, the circuits exhibit complex dynamical responses and dynamical properties of the circuits can be characterized through Farey arithmetic and fractal dimensions of their devil´s staircases. Several interesting properties of the circuits are illustrated through bifurcation diagrams, phase plane and time series responses.