A family of hyperchaotic multi-scroll attractors in Rn

Abstract In this work, we present a mechanism how to yield a family of hyperchaotic multi-scroll systems in R n 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 R 3 to hyperchaotic multi-scroll systems in R n , n ⩾ 4 . An illustrative example of synchronizing a communication system is given based on the developed theory.

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