Boundedness of a Class of Complex Lorenz Systems

Abstract

The estimate of the ultimate bound for a dynamical system is an important problem, which is useful for chaos control and synchronization. In this paper, the estimated ultimate bound of a class of complex Lorenz systems is provided, which extends the parameter regions identified in the current literature on this problem. Based on these results, a kind of complex Lorenz-type systems is constructed, which might have many or infinitely many strange nonchaotic attractors, chaotic attractors, or an infinitely-many-scroll attractor.