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Using covariant Lyapunov vectors to quantify high-dimensional chaos with a conservation law
1Department of Mechanical Engineering, Virginia Tech, Blacksburg, Virginia 24061, USA.
Physical Review. E
|December 20, 2023
Summary
We studied chaotic systems using covariant Lyapunov vectors (CLVs). A conservation law was found to delocalize CLVs, affecting their spatial variation and entanglement with neighbors.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Statistical physics
Background:
- Investigating high-dimensional chaos in coupled map lattices is crucial for understanding complex systems.
- Covariant Lyapunov vectors (CLVs) provide insights into the stability and dynamics of chaotic systems.
- Understanding the interplay between spatial localization and dynamical properties is key.
Purpose of the Study:
- To explore the high-dimensional chaos of diffusively coupled tent maps using CLVs.
- To analyze the relationship between physical space dynamics and tangent space dynamics described by CLVs.
- To investigate the impact of a conservation law on the spatial localization and entanglement of CLVs.
Main Methods:
- Utilizing covariant Lyapunov vectors (CLVs) and covariant Lyapunov exponents.
- Analyzing the tangent space splitting into physical and transient modes.
- Introducing and varying a parameter controlling the strength of a conservation law.
Main Results:
- The splitting of tangent space into physical and transient modes was consistently observed.
- Leading CLVs were generally spatially localized, becoming less localized with increasing Lyapunov index.
- A conservation law was found to delocalize the spatial variation of CLVs.
- The presence of a conservation law reduced the entanglement of leading CLVs with their neighbors.
Conclusions:
- CLV dynamics are intrinsically linked to the physical space dynamics in coupled chaotic systems.
- Conservation laws significantly alter the spatial properties of CLVs, leading to delocalization.
- The study reveals how conservation laws impact information propagation and stability in chaotic lattices.
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