Dynamics of the stochastic Lorenz chaotic system with long memory effects.
Dynamics of the stochastic Lorenz chaotic system with long memory effects.
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DOI：
10.1063/1.4937726
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发表时间：
2015-12
期刊：
影响因子：
2.9
通讯作者：
Caibin Zeng;Qigui Yang
中科院分区：
文献类型：
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作者：
Caibin Zeng;Qigui Yang
关于分数噪声随机系统的遍历动力学，人们似乎知之甚少。本文通过具有长记忆效应的随机Lorenz混沌系统来研究这种长时间的动力学行为。通过截断技术，证明了SLCS生成一个连续随机动力系统Λ。基于Krylov-Bogoliubov准则，进一步建立了所需的李雅普诺夫函数，以保证Λ的不变测度的存在性.同时，通过强Feller性质证明了Λ的不变测度的唯一性，并给出了一个不可约性证明.因此，SLCS只有一个自适应平稳解。
Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.