DISCRETE CHAOTIC DYNAMICS FROM CHUA'S OSCILLATOR: CHUA MACHINES

In previous work, the authors explored the parameter space for Chua's circuit and its generalizations, discovering new routes to chaos, and nearly a thousand new attractors. These were obtained by varying the parameters of the physical circuit and of systems derived from it. Here, we present a novel class of computational system that does not respect the classical constraints in Chua's circuit, and that generates chaotic dynamics via an iterative process based on discrete versions of the equations for Chua's circuit and its variants. We call these systems Chua Machines. After presenting the chaotic dynamics, we provide a formal description of Chua Machines and a Gallery of 222 3D images, illustrating their dynamics. We discuss the method used to discover these systems and the metrics applied in the exploration of their parameter space and offer examples of highly complex bifurcation maps, together with images showing how patterns can evolve with time, or vary significantly changing the values of one of the parameters. Finally, we present a detailed analysis of qualitative changes in a Chua Machine as it traverses the parameter space of the bifurcation map. The evidence suggests that these dynamics are even richer and more complex than their counterpart in the continuous domain.