Transfer maps and return maps for piecewise‐linear three‐region dynamical systems

Abstract Techniques formerly developed in the theory of Poincaré half‐maps are modified and applied to the three‐region piecewise‐linear continuous dynamical system associated with Chua's circuit. Both transfer and return maps, induced by the trajectories inside the intermediate region in state space, are formulated as implicit equations. the boundaries of the domains of these maps are determined explicitly, using the method for calculating the initial points of touching trajectories subject to appropriate switching dynamics. A charting of the canonical parameter space of the dynamics that acts on the intermediate region is indicated. Among other things, this chart reveals the existence of new types of chaotic attractors different from the double scroll and Rössler attractors previously discovered from Chua's circuit.