Dynamics of the stochastic Lorenz-Haken system

作者：Li, Lijie; Feng, Yu; Liu, Yongjian^*

来源：Chaos Solitons & Fractals, 2016, 91: 670-678.

DOI：10.1016/j.chaos.2016.09.003

• Stochastic asymptotic behavior
• Exponential attractive set
• Stochastic Lorenz-Halcen system
• Random attractor

In this paper, the dynamics of the stochastic Lorenz-Haken system are discussed, and some new results are presented. Firstly, the asymptotic behavior of the stochastic Lorenz-Haken system is analyzed. The interesting thing is that all of solutions of the system can tend to zero under some parameters conditions and never go through the hyper-plane x = 0 as the large time. Secondly, the globally exponential attractive set and a four-dimensional ellipsoidal ultimate boundary are derived. The two-dimensional parabolic ultimate bound with respect to x - u is also established. The numerical results to estimate the ultimate boundary are also presented for verification. Finally, the random attractor set and the bifurcation phenomenon for the system are analyzed.

• 出版日期2016-10
• 单位玉林师范学院