# Collective Lyapunov modes

@article{Takeuchi2013CollectiveLM, title={Collective Lyapunov modes}, author={Kazumasa A. Takeuchi and Hugues Chat'e}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2013}, volume={46} }

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…

## 18 Citations

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Abstract
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The analysis of turbulent GCMs with positive multipliers suggests that a universal convergence law for the LE cannot be taken for granted in general GCMs, and finds a power-law scaling of λ_{∞}-λ(N)≃c/N^{γ}, where γ is a parameter-dependent exponent in the range 0<γ≤1.

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L et us apply our newly acquired tools to the fundamental diagnostics in dynamics: Is a given system ‘chaotic’? And if so, how chaotic? If all points in example 2.3 a neighborhood of a trajectory…

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