Chaos control for multi scroll chaotic attractors generated by introducing a bipolar sigmoid function series
In this paper, a bipolar sigmoid function series is proposed to generate 1 D (one dimensional) and 2 D (two dimensional) multi scroll chaotic attractors. The nonlinear dynamical behaviors of 1 D and 2 D multi scroll chaotic systems are analyzed, including the equilibrium points, invariance, dissipation, Lyapunov exponents, fractional dimension and Poincare map. In addition, backstepping controllers are used to stabilize the 1 D and 2 D multi scroll chaotic systems. The results show that the 1 D and 2 D multi scroll chaotic attractors can be generated by introducing the bipolar sigmoid function series. The mechanism for generating multi scroll chaotic attractors is as follows: The equilibrium points with index 2 (type two) are responsible for generating scrolls, and the equilibrium points with index 1 (type one) are responsible for connecting these scrolls. The chaotic behaviors in the 1 D and 2 D multi scroll chaotic systems are stabilized to some equilibrium points using the backstepping controllers, without determining the desired targeting orbits beforehand.
Indian Journal of Physics