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Non-self-averaging Lyapunov exponent in random conewise linear systems
Théo Dessertaine1,2, Jean-Philippe Bouchaud2,3
1LadHyX UMR CNRS 7646, Ecole polytechnique, 91128 Palaiseau Cedex, France.
Physical Review. E
|June 16, 2022
Summary
This study explores multidimensional conewise linear dynamics. The Lyapunov exponent is non-self-averaging for large systems, showing apparent stability and instability depending on conditions.
Area of Science:
- Dynamical Systems
- Mathematical Physics
- Statistical Mechanics
Background:
- Investigates dynamics near cusplike equilibria.
- Models local linear evolution using random matrices.
Purpose of the Study:
- Analyze multidimensional conewise linear dynamics.
- Examine Lyapunov exponent behavior in large systems.
- Understand finite N effects and cone trapping.
Main Methods:
- Employs a simple model for conewise linear dynamics.
- Utilizes random matrix theory for system evolution.
- Connects to the random diffusion persistence problem.
Main Results:
- Lyapunov exponent is non-self-averaging as N approaches infinity.
- Demonstrates apparent stability and instability for the same system.
- Identifies cone trapping phenomena due to finite N effects.
Conclusions:
- The non-self-averaging nature of the Lyapunov exponent is a key finding.
- Finite N effects introduce unique dynamical behaviors like cone trapping.
- The model provides insights into complex systems with piecewise linear dynamics.
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