SUMMARYIn this letter we investigate, via numerical simulations, the parameter-space of the set of autonomous firstorder differential equations of a Chua circuit. We show that this parameter-space presents self-organized periodic structures immersed in a chaotic region, forming a single spiral structure that coils up around a focal point. Additionally, bifurcation diagrams are used to show that those periodic structures also organize themselves in period-adding cascades, along specific directions that point towards this same focal point.
We report numerical results on the existence of periodic structures embedded in chaotic and hyperchaotic regions on the Lyapunov exponent diagrams of a 4-dimensional Chua system. The model was obtained from the 3-dimensional Chua system by the introduction of a feedback controller. Both the largest and the second largest Lyapunov exponents were considered in our colorful Lyapunov exponent diagrams, and allowed us to characterize periodic structures and regions of chaos and hyperchaos. The shrimp-shaped periodic structures appear to be malformed on some of Lyapunov exponent diagrams, and they present two different bifurcation scenarios to chaos when passing the boundaries of itself, namely via period-doubling and crisis. Hyperchaos-chaos transition can also be observed on the Lyapunov exponent diagrams for the second largest exponent.
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