Controlling Dynamics to Coexisting Periodic Solutions or Equilibrium Points of the n-Scroll Modified Chua’s Circuit

Abstract

The modified Chua’s circuit, which is first order differentiable, has degree-of-discontinuity [Formula: see text]. It has [Formula: see text] equilibrium points, including two boundary equilibrium points. For them, except boundary equilibrium points, we obtain in theory, conditions under which Hopf bifurcations exist, which implies coexisting periodic solutions. At the same time, we also show that equilibrium points are asymptotically stable when system parameters are within some limits. Furthermore, we theoretically design a linear feedback controller, which will not change the equilibrium points, with appropriate control parameters to control the dynamical behaviors including chaos to these periodic solutions or equilibrium points, and we verify it by numerical simulations.