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Updated: Jun 19, 2026
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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Emerging attractors and the transition from dissipative to conservative dynamics
Christian S Rodrigues1, Alessandro P S de Moura, Celso Grebogi
1Department of Physics, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom. c.rodrigues@abdn.ac.uk
Summary
Chaotic dynamical systems exhibit complex basin boundary structures. This study reveals that as dissipation decreases, the number of periodic attractors grows according to a power law, with effective invariants governing dynamics at small scales.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Chaos Theory
Background:
- Basin boundary topology is crucial for predicting final states in chaotic systems.
- Dissipative systems near the Hamiltonian limit exhibit unique dynamic behaviors.
Purpose of the Study:
- Investigate the dynamics of dissipative systems as dissipation approaches zero.
- Analyze structural changes in basin boundaries and the emergence of periodic attractors.
- Explore the role of effective dynamical invariants in these systems.
Main Methods:
- Numerical simulations of dissipative systems.
- Analysis of basin boundary structures.
- Power law fitting to describe attractor growth.
- Examination of dynamics at small scales.
Main Results:
- A power law with a nontrivial exponent quantifies the increase in periodic attractors as damping decreases.
- Effective dynamical invariants govern dynamics at small scales.
- The measure of these invariants is dependent on phase space region and scale.
Conclusions:
- The number of periodic attractors in dissipative systems scales with damping.
- Effective dynamical invariants are relevant even in dissipative systems, not just conservative ones.
- Understanding these invariants is key to characterizing complex dynamics.
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