Multi-wing butterfly attractors from the modified Lorenz systems

Based on the sawtooth wave function, this paper initiates an approach for generating novel multi-wing butterfly chaotic attractors from the generalized first and second types of modified Lorenz systems. Our theoretical analysis shows that every index-2 saddle-focus equilibrium corresponds to a unique wing in the butterfly attractors. Compared with the traditional ring-shaped multiscroll Lorenz chaotic attractors, the proposed multi-wing butterfly chaotic attractors are much easier to be constructed and implemented by analog circuits. Furthermore, a module-based unified circuit diagram is designed for realizing various multi-wing attractors.