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Updated: Jul 15, 2026
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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Recurrence analysis of strange nonchaotic dynamics.
E J Ngamga1, A Nandi, R Ramaswamy
1Nonlinear Dynamics Group, Institute of Physics, University of Potsdam, Potsdam 14415, Germany.
Summary
We developed new methods to detect transitions between quasiperiodic and chaotic motion using strange nonchaotic attractors (SNAs). These techniques reliably identify complex dynamics, even with noise, in experimental data.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Complex systems analysis
Background:
- Distinguishing between quasiperiodic and chaotic dynamics is crucial in nonlinear systems.
- Strange nonchaotic attractors (SNAs) represent a unique state between order and chaos.
- Existing methods often struggle to detect transitions involving SNAs, particularly fractalization.
Purpose of the Study:
- To present novel methods for detecting transitions to and from strange nonchaotic attractors (SNAs).
- To demonstrate the effectiveness of these methods in analyzing quasiperiodically forced discrete maps.
- To provide robust tools for analyzing experimental time series data exhibiting complex dynamics.
Main Methods:
- Recurrence time analysis to quantify the time systems take to revisit previous states.
- Quantification of trajectory synchronization on SNAs.
- Application to representative quasiperiodically forced discrete maps.
Main Results:
- Successfully detected transitions to SNAs and from SNAs to chaos.
- Recurrence analysis effectively identified the fractalization transition to SNAs, a challenge for existing methods.
- The developed methods demonstrated robustness against additive noise.
Conclusions:
- The presented methods offer reliable detection of transitions involving SNAs.
- Recurrence analysis is particularly effective for identifying the fractalization transition.
- These techniques are suitable for analyzing complex dynamics in experimental time series data.
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