Dynamics of the stochastic Lorenz-Haken system

被引:3
作者
Li, Lijie [1 ]
Feng, Yu [1 ]
Liu, Yongjian [1 ]
机构
[1] Yulin Normal Univ, Guangxi Coll & Univ Key Lab Complex Syst Optimiza, Yulin 537000, Peoples R China
基金
中国国家自然科学基金;
关键词
Stochastic asymptotic behavior; Exponential attractive set; Stochastic Lorenz-Halcen system; Random attractor; INVARIANT SET; MODEL; STABILITY;
D O I
10.1016/j.chaos.2016.09.003
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码:670 / 678
页数:9
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