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Related Experiment Video

Updated: May 10, 2026

Sealable Femtoliter Chamber Arrays for Cell-free Biology

Sealable Femtoliter Chamber Arrays for Cell-free Biology

Published on: March 11, 2015

Intermittency in relation with 1/f noise and stochastic differential equations.

J Ruseckas¹, B Kaulakys

¹Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania. julius.ruseckas@tfai.vu.lt

Chaos (Woodbury, N.Y.)

|July 5, 2013

Summary

This summary is machine-generated.

This study reveals a new mechanism for generating 1/f noise in nonlinear dynamical systems. Unlike on-off intermittency, this mechanism occurs when the transverse Lyapunov exponent is zero, offering insights into 1/f(β) noise generation.

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Last Updated: May 10, 2026

Sealable Femtoliter Chamber Arrays for Cell-free Biology

Sealable Femtoliter Chamber Arrays for Cell-free Biology

Published on: March 11, 2015

Area of Science:

Nonlinear Dynamics
Complex Systems Analysis
Statistical Physics

Background:

On-off intermittency, a model of intermittent behavior, exhibits 1/√f power-law noise in its power spectral density (PSD).
This phenomenon arises from time-dependent forcing of bifurcation parameters through a bifurcation point.

Purpose of the Study:

To investigate a novel intermittency mechanism in nonlinear dynamical systems with an invariant subspace.
To explore noise generation when the transverse Lyapunov exponent is zero, contrasting with traditional on-off intermittency.

Main Methods:

Analysis of nonlinear dynamical systems exhibiting an invariant subspace.
Investigation of systems where the transverse Lyapunov exponent is zero.
Characterization of the power spectral density (PSD) of deviations from the invariant subspace.

Main Results:

Demonstration that such systems can exhibit 1/f(β) noise across a broad frequency range.
Identification of a mechanism for 1/f noise generation distinct from on-off intermittency.
Establishment and analysis of connections to stochastic differential equations that generate 1/f(β) noise.

Conclusions:

Nonlinear dynamical systems with a transverse Lyapunov exponent of zero can generate 1/f noise.
This finding expands our understanding of noise generation mechanisms in complex systems.
The study provides a framework for analyzing 1/f(β) noise through stochastic differential equations.