Complex Dynamical Behaviors of Lorenz-Stenflo Equations

Fuchen Zhang,Min Xiao

doi:10.3390/math7060513

Abstract

A mathematical chaos model for the dynamical behaviors of atmospheric acoustic-gravity waves is considered in this paper. Boundedness and globally attractive sets of this chaos model are studied by means of the generalized Lyapunov function method. The innovation of this paper is that it not only proves this system is globally bounded but also provides a series of global attraction sets of this system. The rate of trajectories entering from the exterior of the trapping domain to its interior is also obtained. Finally, the detailed numerical simulations are carried out to justify theoretical results. The results in this study can be used to study chaos control and chaos synchronization of this chaos system.

Highlights

Dynamical behaviors of the Lorenz-Stenflo system, such as periodicity [19,20], bifurcation phenomenon [21,22], synchronization behaviors chaotic have been studied by many researchers
The main goal of this paper is to study the Lorenz-Stenflo chaos system, describing the dynamical behavior of atmospheric acoustic-gravity waves
A family of hyperelliptic estimates of the ultimate bound and positively invariant set for the Lorenz-Stenflo system is obtained by means of the generalized

Summary

Introduction

In 1963, E.N. Lorenz [1] obtained the famous Lorenz chaotic system to describe weather changes. In 1996, the physicist Lennart Stenflo [18] obtained a new four-dimensional continuous-time dynamical chaotic system by adding a new variable w to the Lorenz system to describe the complex dynamical behaviors of the atmospheric acoustic-gravity waves. It is important for us to study acoustic gravity waves because they are associated with minor weather changes and large-scale phenomena. Dynamical behaviors of the Lorenz-Stenflo system, such as periodicity [19,20], bifurcation phenomenon [21,22], synchronization behaviors chaotic have been studied by many researchers. Globally bounded and provides a series of global attraction sets of this Lorenz-Stenflo system. The rate of trajectories entering from the exterior of the trapping domain to its interior is obtained

Boundedness and Global Attraction

Conclusions