Collective Lyapunov modes
Kazumasa A. Takeuchi, Hugues Chat\'e
TL;DR
This paper identifies collective Lyapunov modes in large chaotic systems using covariant Lyapunov vectors, linking them to collective dynamics and addressing chaos extensivity.
Contribution
It introduces the concept of collective Lyapunov modes and connects them to Perron-Frobenius modes in globally-coupled systems, advancing understanding of collective chaos.
Findings
Existence of collective Lyapunov modes in large chaotic systems
Connection between collective modes and Perron-Frobenius modes
Insights into the effective dimension and extensivity of collective chaos
Abstract
We show, using covariant Lyapunov vectors in addition to standard Lyapunov analysis, that there exists a set of collective Lyapunov modes in large chaotic systems exhibiting collective dynamics. Associated with delocalized Lyapunov vectors, they act collectively on the trajectory and hence characterize the instability of its collective dynamics. We further develop, for globally-coupled systems, a connection between these collective modes and the Lyapunov modes in the corresponding Perron-Frobenius equation. We thereby address the fundamental question of the effective dimension of collective dynamics and discuss the extensivity of chaos in presence of collective dynamics.
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