Estimating the Ultimate Bounds and Positively Invariant Sets for a Class of General Lorenz-type New Chaotic Systems

Abstract

To estimate the ultimate bound and positively invariant set of a dynamic system is an important but quite challenging task. In this paper, we attempt to investigate the ultimate bounds and positively invariant sets for a class of more general Lorenz-type new chaotic systems. We derive some ellipsoidal estimates of the globally exponentially attractive set and positively invariant set of the general Lorenz-type new system for all the positive values of its parameters via the generalized Lyapunov function theory. Furthermore, the estimations derived here contain the results given in as special cases and can lead to a series of new estimations.