A family of hyperchaotic multi-scroll attractors in Rn
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In this work, we present a mechanism how to yield a family of hyperchaotic multi-scroll systems in Rn based on unstable dissipative systems. This class of systems is constructed by a switching control law changing the equilibrium point of an unstable dissipative system. For each equilibrium point presented in the system a scroll emerges. The switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor. Thus, if two systems display different numbers of scrolls, they have different switching control laws. This paper also presents a generalized theory that explains different approaches such as hysteresis and step functions from a unified viewpoint, extending the concept of chaos in R3 to hyperchaotic multi-scroll systems in Rn,n≥4. An illustrative example of synchronizing a communication system is given based on the developed theory. © 2014 Elsevier Inc. All rights reserved.
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Chaos theory; Multi-scroll attractors; Piecewise-linear analysis; Piecewise-linear techniques; Switched systems; Switching functions; System design Dissipative systems; Equilibrium point; Generalized theory; Multi-scroll attractors; Multi-scroll systems; Piecewise-linear; Switched system; Switching Control; Chaos theory; Control theory; Dynamical systems; Energy dissipation; Piecewise linear techniques; Switching functions; Systems analysis; Switching systems
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