Generalized multistable structure via chaotic synchronization and preservation of scrolls

Switched systems are capable of generating chaotic multi-scroll behavior in R3 by means of a control signal. This signal regulates an equilibrium position of the system and is defined according to the number of scrolls that is displayed by the attractor. Thus, if two systems are controlled by different signals, they exhibit a different number of scrolls. Multistability can be created by a pair of unidirectionally coupled unstable dissipative switched linear systems. A theoretical study of this phenomenon is performed with the jerky equations. Generalized synchronization is observed in numerical simulations of the master-salve system with different control signals. The proposed configuration preserves the number of scrolls and can possess an arbitrary large number of coexisting chaotic multi-scroll attractors.