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Torus fractalization and intermittency.

Sergey P Kuznetsov¹

¹Institute of Radio-Electronics, Russian Academy of Sciences, Zelenaya 38, Saratov 410019, Russian Federation.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 22, 2002

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Researchers studied intermittency onset with quasiperiodic forces, focusing on torus-fractalization. They found universal scaling constants and identified transitions to chaotic or nonchaotic attractors.

Area of Science:

Nonlinear Dynamics
Chaos Theory
Statistical Physics

Background:

Intermittency and bifurcation transitions are key phenomena in nonlinear systems.
The Pomeau-Manneville mechanism describes intermittency onset in certain dynamical systems.
Quasiperiodic forcing introduces complex dynamics not present in periodic forcing.

Purpose of the Study:

To investigate bifurcation transitions and intermittency onset under quasiperiodic forcing.
To analyze the torus-fractalization (TF) critical point.
To develop a renormalization group (RG) analysis for the TF critical point.

Main Methods:

Generalization of the Pomeau-Manneville mechanism for quasiperiodic forces.
Renormalization group (RG) analysis applied to the torus-fractalization critical point.

Related Experiment Videos

Investigation of fractional-linear functions and their fixed-point solutions.

Main Results:

A nontrivial fixed-point solution for the RG equation was found for the golden mean rotation number.
Universal constants governing phase space (alpha, beta) and parameter space (delta1, delta2) scaling were computed.
An analogy with the Harper equation revealed unique transition characteristics.

Conclusions:

The study characterizes the torus-fractalization critical point under quasiperiodic forcing.
Transitions can lead to intermittent chaotic regimes or strange nonchaotic attractors depending on driving amplitude.
The findings provide insights into complex dynamics and bifurcations in driven systems.