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Characterizing dynamics with covariant Lyapunov vectors.
A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows us to address fundamental questions such as the degree of
Deciphering Interactions in Moving Animal Groups
Using video tracks of fish shoal in a tank, it is shown how a careful, incremental analysis at the local scale allows for the determination of the stimulus/response function governing an individual's moving decisions, yielding a novel schooling model whose parameters are all estimated from data.
Collective motion of self-propelled particles interacting without cohesion.
The onset of collective motion in Vicsek-style self-propelled particle models in two and three space dimensions is studied in detail and shown to be discontinuous (first-order-like), and the properties of the ordered, collectively moving phase are investigated.
Modeling collective motion: variations on the Vicsek model
We argue that the model introduced by Vicsek et al. in which self-propelled particles align locally with neighbors is, because of its simplicity, central to most studies of collective motion or
Covariant Lyapunov vectors
Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of
Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
We describe a generic theoretical framework, denoted as the Boltzmann-Ginzburg-Landau approach, to derive continuous equations for the polar and/or nematic order parameters describing the large scale
Simple model for active nematics: quasi-long-range order and giant fluctuations.
We propose a simple microscopic model for active nematic particles similar in spirit to the Vicsek model for self-propelled polar particles. In two dimensions, we show that this model exhibits a
Large-scale collective properties of self-propelled rods.
This work studies the collective properties of constant-speed polar point particles interacting locally by nematic alignment in the presence of noise to reveal long-range nematic order, phase separation, and space-time chaos mediated by large-scale segregated structures.
Large-scale chaos and fluctuations in active nematics.
It is proved, in particular, that the chaos stems from the generic instability of the band solution of the hydrodynamic equations of the particle model, and that the giant number fluctuations observed in the chaotic phase are a trivial consequence of density segregation.
Hyperbolicity and the effective dimension of spatially extended dissipative systems.
Using covariant Lyapunov vectors, it is argued that N can be interpreted as the number of effective degrees of freedom, which has to be taken into account in numerical integration and control issues.