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Dynamics of the stochastic Lorenz-Haken system

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  • Li, Lijie
  • Feng, Yu
  • Liu, Yongjian

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.

Suggested Citation

  • Li, Lijie & Feng, Yu & Liu, Yongjian, 2016. "Dynamics of the stochastic Lorenz-Haken system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 670-678.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:670-678
    DOI: 10.1016/j.chaos.2016.09.003
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    References listed on IDEAS

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