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Published on: March 30, 2017
Intermittency transitions to strange nonchaotic attractors in a quasiperiodically driven duffing oscillator
Venkatesan1, Lakshmanan, Prasad
1Center for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirappalli, 620 024, India.
Summary
Strange nonchaotic attractors (SNAs) in a driven Duffing oscillator arise from intermittency transitions, specifically quasiperiodic saddle-node and subharmonic bifurcations. Analysis using Lyapunov exponents characterizes these ubiquitous attractors in quasiperiodically driven systems.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Bifurcation Theory
Background:
- Strange nonchaotic attractors (SNAs) are complex dynamical objects observed in quasiperiodically driven systems.
- Understanding the formation mechanisms of SNAs is crucial for characterizing system behavior.
Purpose of the Study:
- Investigate the creation mechanisms of SNAs in a two-frequency parametrically driven Duffing oscillator.
- Focus on intermittency transitions as pathways to SNA formation.
- Characterize intermittent attractors using Lyapunov measures.
Main Methods:
- Analysis of a two-frequency parametrically driven Duffing oscillator.
- Study of intermittency transitions, including quasiperiodic saddle-node (type-I) and subharmonic (type-III) bifurcations.
- Characterization using Lyapunov exponents (largest nontrivial and finite-time) and their variances.
Main Results:
- SNAs are generated through quasiperiodic saddle-node bifurcations (type-I intermittency).
- SNAs are also generated through quasiperiodic subharmonic bifurcations (type-III intermittency).
- The behavior of Lyapunov exponents and their distributions confirm the intermittent nature of these attractors.
Conclusions:
- Intermittency transitions are key mechanisms for SNA creation in this system.
- The identified SNA regions are mapped in the Duffing system's phase diagram.
- These findings contribute to understanding the prevalence of SNAs in quasiperiodically driven systems.
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