A class of Chua-like systems with only two saddle-foci of different type

Abstract

Abstract Since the reported Chua’s system, several generalizations of this system have been presented, these approaches include new equilibria in order to obtain three or more scrolls in the attractor. One of these generalizations requires at least the same number of saddle-foci with local two-dimensional unstable manifolds as the desired number of scrolls. In this work, we present the generation of a double-scroll chaotic attractor called Chua-like system. Once that an equilibrium point has been removed from the Chua’s system and there are only two saddle-foci of different class, i.e. the dimension of one of the local unstable manifolds is one while the other is of dimension two. The new class is constructed based on the existence of a heteroclinic loop by linear affine systems with two saddle-focus equilibrium points of different type. Furthermore, the chaotic behavior of the proposed system is tested by the maximum Lyapunov exponent and the 0 — 1 chaos test.