Two-segment bistability and basin structure in three-segment PWL circuits

Of all the piecewise-linear circuits known so far which exhibit two stable states, it is typical that their resistor characteristics each have at least three segments. The authors show that bistability cannot be achieved via a two-segment characteristic in the plane. On the other hand, complicated bistable behaviour, including chaotic attractors, can occur locally at the boundary of two linear regions in higher-dimensional circuits. By using a three-segment characteristic, at least three attractors can be generated in the planar Lienard oscillator and five attractors are exhibited in three-dimensional Chua´s circuit. Basin structure of the corresponding attractors is examined using numerical simulations. The use of basin delineation in the triggering of multistable circuits is shown