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Characterizing strange nonchaotic attractors
Arkady S. Pikovsky1, Ulrike Feudel
1Max-Planck-Arbeitsgruppe "Nichtlineare Dynamik," Universitat Potsdam, Potsdam, Germany.
Chaos (Woodbury, N.Y.)
|March 1, 1995
Summary
This study introduces two methods to characterize strange nonchaotic attractors in nonlinear systems. Phase sensitivity analysis reveals these attractors appear when positive Lyapunov exponents have a nonzero probability.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Mathematical Physics
Background:
- Strange nonchaotic attractors are characteristic of quasiperiodically driven nonlinear systems.
- Understanding these attractors is crucial for analyzing complex system behaviors.
Purpose of the Study:
- To propose novel methods for characterizing strange nonchaotic attractors.
- To investigate the relationship between phase sensitivity and system dynamics.
Main Methods:
- Bifurcation analysis of systems with periodic approximations of quasiperiodic forcing.
- Calculation of a phase sensitivity exponent to measure response to external force phase changes.
Main Results:
- Phase sensitivity is a key indicator of strangeness in these attractors.
- Phase sensitivity emerges when there's a probability of positive local Lyapunov exponents.
Conclusions:
- The proposed methods offer effective characterization of strange nonchaotic attractors.
- Phase sensitivity is directly linked to the occurrence of positive local Lyapunov exponents, defining attractor strangeness.