786 citations · 2.4k across the 106 of their papers we have counts for
6 papers · 1 filter
Differential positivity characterizes one-dimensional normally hyperbolic attractors
Fulvio Forni, Alexandre Mauroy, Rodolphe Sepulchre
The paper shows that normally hyperbolic one-dimensional compact attractors of smooth dynamical systems are characterized by differential positivity, that is, the pointwise infinit…
A three-scale model of spatio-temporal bursting
Alessio Franci, Rodolphe Sepulchre
We study spatio-temporal bursting in a three-scale reaction diffusion equation organized by the winged cusp singularity. For large time-scale separation the model exhibits travelin…
A spectral characterization of nonlinear normal modes
Giuseppe Ilario Cirillo, Alexandre Mauroy, Ludovic Renson +2
This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman opera…
An operator-theoretic approach to differential positivity
A. Mauroy, F. Forni, R. Sepulchre
Differentially positive systems are systems whose linearization along trajectories is positive. Under mild assumptions, their solutions asymptotically converge to a one-dimensional…
Sparse plus low-rank autoregressive identification in neuroimaging time series
Raphaël Liégeois, Bamdev Mishra, Mattia Zorzi +1
This paper considers the problem of identifying multivariate autoregressive (AR) sparse plus low-rank graphical models. Based on the corresponding problem formulation recently pres…
On the Projective Geometry of Kalman Filter
Francesca Paola Carli, Rodolphe Sepulchre
Convergence of the Kalman filter is best analyzed by studying the contraction of the Riccati map in the space of positive definite (covariance) matrices. In this paper, we explore…