A novel approach for generating multi-direction multi-double-scroll attractors

It is a common phenomenon that multi-scroll attractors are realized by introducing the various nonlinear functions with multiple breakpoints in double-scroll chaotic systems. Differently, this paper introduces a new systematic method for generating multi-direction multi-double-scroll (MDMDS) chaotic attractors without changing the original nonlinear functions. By using the multi-pulse control technique in a three-dimensional double-scroll chaos system, a new family of double-scroll grid attractors can be generated, including 1-D double-scroll, 2-D double-scroll, and 3-D double-scroll chaotic attractors. Theoretical analysis and numerical simulations show the MDMDS can be generated by constructing pulsed excitation in corresponding state variable directions (1-D), plane (2-D), or space (3-D). Mean while, it is possible to increase the number of scrolls in all state variable directions by adding the number of pulsed excitation. Furthermore, the proposed approach is applied in Chua's circuit; a series of MDMDS attractors are presented. Finally, corresponding realization circuit is designed using CFOAs. The obtained Pspice results are in agreement with numerical simulation results, which verify the availability and feasibility of this method.