Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania.
Chaos. 2013 Jun;23(2):023102. doi: 10.1063/1.4802429.
One of the models of intermittency is on-off intermittency, arising due to time-dependent forcing of a bifurcation parameter through a bifurcation point. For on-off intermittency, the power spectral density (PSD) of the time-dependent deviation from the invariant subspace in a low frequency region exhibits 1/√f power-law noise. Here, we investigate a mechanism of intermittency, similar to the on-off intermittency, occurring in nonlinear dynamical systems with invariant subspace. In contrast to the on-off intermittency, we consider the case where the transverse Lyapunov exponent is zero. We show that for such nonlinear dynamical systems, the power spectral density of the deviation from the invariant subspace can have 1/f(β) form in a wide range of frequencies. That is, such nonlinear systems exhibit 1/f noise. The connection with the stochastic differential equations generating 1/f(β) noise is established and analyzed, as well.
一种间歇性模型是开关间歇性，它是由于分岔参数的时变驱动通过分岔点而产生的。对于开关间歇性，在低频区域中，从不变子空间的时变偏离的功率谱密度（PSD）表现出 1/√f 幂律噪声。在这里，我们研究了一种类似于开关间歇性的间歇性机制，它发生在具有不变子空间的非线性动力系统中。与开关间歇性不同，我们考虑横向李亚普诺夫指数为零的情况。我们表明，对于这样的非线性动力系统，从不变子空间的偏离的功率谱密度在很宽的频率范围内可以具有 1/f(β)形式。也就是说，这样的非线性系统表现出 1/f 噪声。还建立并分析了与产生 1/f(β)噪声的随机微分方程的联系。
