GENERATION OF A FOUR-WING CHAOTIC ATTRACTOR BY TWO WEAKLY-COUPLED LORENZ SYSTEMS

Abstract

This paper presents a novel chaotic four-wing attractor generated by coupling two identical Lorenz systems. An analysis of the proposed system shows that its equilibria have certain symmetries with respect to specific coordinate planes and the eigenvalues of the associated Jacobian matrices exhibit the property of similarity. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings of this new attractor are located around four equilibria with four unstable complex-conjugate eigenvalues. A generalization of the proposed system to realize an eight-wing attractor is also described.