Controlling the chaotic n-scroll Chua's circuit

In this paper, controlling chaos in the chaotic n-scroll Chua's circuit is studied. The approach taken is to use feedback of a single state variable in a simple PD (proportional and differential) format. First, the unstable fixed points in the n-scroll Chua's circuit are classified into two different types according to the characteristics of the eigenvalues of the linearized system matrix at the fixed points. Then, the controllability of these two-types of fixed points is studied. Theoretical analysis shows that the first type of unstable fixed points can be stabilized, at which Hopf bifurcation can also be generated. Control results of the n-scroll Chua's circuit are then demonstrated. Both theoretical analysis and numerical simulation results show that the proposed chaos control method is indeed effective.