Bounds for the fast–slow Lorenz–Stenflo system

Abstract

In this paper, the dynamical behaviors of the fast–slow Lorenz–Stenflo system are considered based on generalized Lyapunov function theory with integral inequalities. Explicit estimations of the ultimate bounds are derived. The meaningful contribution of this article is that not only do we get the ultimate boundedness of solutions of the fast–slow Lorenz–Stenflo system, but we also get the rate of the trajectories of the system going from the exterior of the trapping set to the interior of the trapping set. Computer simulation results show that the proposed method is effective.