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Although the globally attractive sets of a hyperchaotic system have important applications in the fields of engineering, science, and technology, it is often a difficult task for the researchers to obtain the globally attractive set of the hyperchaotic systems due to the complexity of the hyperchaotic systems. Therefore, we will study the globally attractive set of a generalized hyperchaotic Lorenz–Stenflo system describing the evolution of finite amplitude acoustic gravity waves in a rotating atmosphere in this paper. Based on Lyapunov-like functional approach combining some simple inequalities, we derive the globally attractive set of this system with its parameters. The effectiveness of the proposed methods is illustrated via numerical examples.

In 1963, Lorenz found the well-known three-dimensional Lorenz model when he studied the dynamics of the atmosphere [

In order to give a better description of the atmosphere, Chen and Liang propose a generalized Lorenz–Stenflo system with six parameters according to the Lorenz–Stenflo system [

The Lyapunov exponents of the dynamical system (

Projection of hyperchaotic attractor of system (

Projection of hyperchaotic attractor of system (

Projection of hyperchaotic attractor of system (

Projection of hyperchaotic attractor of system (

In this paper, all the simulations are carried out by using fourth-order Runge-Kutta Method with time-step

The rest of this paper is organized as follows. In Section

For any

Define the following Lyapunov-like function:

And we can get

This completes the proof.

Suppose that

Let

Define the following functions:

The proof is complete.

(i) In particular, let us take

Suppose that

Let

(ii) Let us take

When

Figure

Localization of hyperchaotic attractor of system (

Localization of hyperchaotic attractor of system (

Localization of hyperchaotic attractor of system (

Localization of hyperchaotic attractor of system (

In this paper, we have investigated some global dynamics of a generalized Lorenz–Stenflo system describing the evolution of finite amplitude acoustic gravity waves in a rotating atmosphere. Based on the Lyapunov method, the globally attractive sets were formulated combining simple inequalities. Finally, numerical examples were presented to show the effectiveness of the proposed method.

All authors have read and approved the final manuscript.

The authors declare that they have no conflicts of interest.

This work is supported by National Natural Science Foundation of China (Grant no. 11501064), the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant no. KJ1500605), the Research Fund of Chongqing Technology and Business University (Grant no. 2014-56-11), China Postdoctoral Science Foundation (Grant no. 2016M590850), Chongqing Postdoctoral Science Foundation Special Funded Project (Grant no. Xm2017174), and the Research Fund of Chongqing Technology and Business University (Grant no. 1752073). The authors thank Professors Jinhu Lu in Institute of Systems Science, Chinese Academy of Sciences, Gaoxiang Yang in Ankang University, Ping Zhou in Chongqing University of Posts and Telecommunications, and Min Xiao in Nanjing University of Posts and Telecommunications for their help.