In the work [Chua, 1992], a deep intuition of its author gave rise to the choice of singularities corresponding to Chua's circuit. Therefore, it is the only one probably exhibiting three saddle points named Chua's singularities in this paper. One of the singularities is a saddle in forward time (dt > 0) of integration, whereas the other two are saddles in backward time (dt < 0) of integration. In the following, the term Chua's Chaos denotes chaos related to Chua's singularities. These singularities are the source of all special surfaces that are the subject of this contribution. We named the surface to which all other surfaces are bound as the Double-Arm Stable Manifold (DASM). The beauty and multifunctionality of this surface represents the unfathomable Intelligence in the sense of [Tolle, 2003]. The presence of the DASM in the state space is a sufficient condition for the generation of Chua's chaos or corresponding periodic windows. Since Chua's singularities are not limited by circuit morphology or the order of state equations, the research on Chua's chaos seems to be still very promising.

One of the most important tasks in the analysis of a non-linear system is lo determine its global behaviour and, in particular, to delineate the domains of attraction for asymptotically stable solutions. Stable manifolds often act as boundary surfaces between such domains in the state space.In this paper the morphology of boundary surfaces is studied in a single member of Chua's circuit family, although the techniques used apply equally well to many other non-linear circuits. On the way, an answer is given to a former question of Matsumoto et a / . concerning boundary surfaces in a chaotic circuit.Dynamical properties of a sequential circuit can be investigated by means of switching between the system's attractors, and boundary surfaces play a crucial role in the process of switching. As an application of the boundary surface techniques, dynamical properties of two models for ternary logic are presented and analysed.

One of the most important tasks in the analysis of a nonlinear system is to determine its global behavior and, in particular, to delineate the domains of attraction for asymptotically stable solutions. Stable manifolds often act as boundary surfaces between such domains in the state space. In this paper the morphology of boundary surfaces is studied in a single member of Chua's circuit family, although the techniques used apply equally well to many other nonlinear circuits. Of all the PWL circuits known so far which exhibit two stable states it is typical that their resistor characteristics each have at least three segments. Although bistability cannot be achieved via a 2-segment characteristic in the plane, complicated bistable behavior, including chaotic attractors, can occur locally at the boundary of two linear regions in the 3-D Chua's circuit, i.e. bistability is achieved with a minimal number of segments. By using a 3-segment characteristic, at least five attractors can be generated. Basin structure of the corresponding attractors is examined using numerical simulations. Period-adding, symmetry-breaking and remerging bifurcation phenomena are observed experimentally and numerically from an extended Chua's circuit. Dynamical properties of sequential circuits can be investigated by means of switching between the system's attractors, and boundary surfaces play a crucial role in the process of switching. The use of basin delineation in the triggering of multistable circuits is shown.

No abstract

No abstract