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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 hyperbolicity, which can be quantified in terms of the transversality of these intrinsic vectors. For spatially extended systems, the covariant Lyapunov vectors… (More)

- Hugues Chaté, Francesco Ginelli, Guillaume Grégoire, Franck Raynaud
- Physical review. E, Statistical, nonlinear, and…
- 2008

We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and shown to be discontinuous (first-order-like). The properties of the ordered, collectively moving phase are investigated. In… (More)

- Jacques Gautrais, Francesco Ginelli, +4 authors Guy Theraulaz
- PLoS Computational Biology
- 2012

Collective motion phenomena in large groups of social organisms have long fascinated the observer, especially in cases, such as bird flocks or fish schools, where large-scale highly coordinated actions emerge in the absence of obvious leaders. However, the mechanisms involved in this self-organized behavior are still poorly understood, because the… (More)

- Hong-liu Yang, Kazumasa A Takeuchi, Francesco Ginelli, Hugues Chaté, Günter Radons
- Physical review letters
- 2009

Using covariant Lyapunov vectors, we reveal a split of the tangent space of standard models of one-dimensional dissipative spatiotemporal chaos: A finite extensive set of N dynamically entangled vectors with frequent common tangencies describes all of the physically relevant dynamics and is hyperbolically separated from possibly infinitely many isolated… (More)

- Anton Peshkov, Igor S Aranson, Eric Bertin, Hugues Chaté, Francesco Ginelli
- Physical review letters
- 2012

We derive a set of minimal and well-behaved nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit… (More)

- Anton Peshkov, Sandrine Ngo, Eric Bertin, Hugues Chaté, Francesco Ginelli
- Physical review letters
- 2012

We derive a hydrodynamic description of metric-free active matter: starting from self-propelled particles aligning with neighbors defined by "topological" rules, not metric zones-a situation advocated recently to be relevant for bird flocks, fish schools, and crowds-we use a kinetic approach to obtain well-controlled nonlinear field equations. We show that… (More)

- Sandrine Ngo, Anton Peshkov, Igor S Aranson, Eric Bertin, Francesco Ginelli, Hugues Chaté
- Physical review letters
- 2014

We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order. These results are obtained from the study of both the well-known (deterministic) hydrodynamic equations… (More)

- Kazumasa A Takeuchi, Hong-liu Yang, Francesco Ginelli, Günter Radons, Hugues Chaté
- Physical review. E, Statistical, nonlinear, and…
- 2011

We show, using covariant Lyapunov vectors, that the tangent space of spatially extended dissipative systems is split into two hyperbolically decoupled subspaces: one comprising a finite number of frequently entangled "physical" modes, which carry the physically relevant information of the trajectory, and a residual set of strongly decaying "spurious" modes.… (More)

- Francesco Ginelli, Fernando Peruani, Markus Bär, Hugues Chaté
- Physical review letters
- 2010

We study, in two space dimensions, the collective properties of constant-speed polar point particles interacting locally by nematic alignment in the presence of noise. This minimal approach to self-propelled rods allows one to deal with large numbers of particles, which exhibit a rich phenomenology distinctively different from all other known models for… (More)

- Francesco Ginelli, Hugues Chaté
- Physical review letters
- 2010

We show that the collective properties of self-propelled particles aligning with their topological (Voronoi) neighbors are qualitatively different from those of usual models where metric interaction ranges are used. This relevance of metric-free interactions, shown in a minimal setting, indicate that realistic models for the cohesive motion of cells, bird… (More)