Dynamics of the stochastic Lorenz-Haken system

Lijie Li, Yu Feng and Yongjian Liu

Chaos, Solitons & Fractals, 2016, vol. 91, issue C, 670-678

Abstract: 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.

Keywords: Stochastic asymptotic behavior; Exponential attractive set; Stochastic Lorenz-Haken system; Random attractor (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:91:y:2016:i:c:p:670-678

DOI: 10.1016/j.chaos.2016.09.003

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