A family of hyperchaotic multi-scroll attractors in RnRn

• A mechanism of constructing a family of hyperchaotic multiscroll attractors in Rn is proposed based on unstable dissipative systems.
• This type of attractors arises from a switching system having at least two hyperbolic unstable equilibrium points.
• Different approaches as hysteresis and step function are described by a unified theory given by unstable dissipative systems.
• An illustrative example of synchronizing a communication system is given based on the developed theory.

In this work, we present a mechanism how to yield a family of hyperchaotic multi-scroll systems in RnRn 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 R3R3 to hyperchaotic multi-scroll systems in Rn,n⩾4Rn,n⩾4. An illustrative example of synchronizing a communication system is given based on the developed theory.