A Versatile Pulse Control Method to Generate Arbitrary Multidirection Multibutterfly Chaotic Attractors

In order to overcome the essential difficulties in conventional nonlinear control with iteratively adjusting multiple parameters, a novel method for designing multidirection multibutterfly chaotic attractors (MDMBCAs) without reconstructing nonlinear functions is proposed. By using a unified pulse control in a modified Lorenz system, a family of complete multibutterfly attractors can be produced, including 1-D, 2-D, and 3-D multibutterfly attractors. Theoretical analysis and numerical simulations show that arbitrary MDMBCA all can be generated by conducting the pulse-control in corresponding state variable direction (1-D), plane (2-D), or space (3-D). Meanwhile, the number of butterfly attractors can be controlled with the number of pulsed excitation. Furthermore, we design a module-based unified realization circuit and arbitrary MDMBCA can be obtained by selecting corresponding pulsed-excitation. Our theoretical analysis, MATLAB simulations and circuit experiments together show the effectiveness and universality of the proposed methodology. It should be especially pointed out that the proposed method is a universal scheme and can be applied in the arbitrary double-wing chaotic system.