306 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Universidade do PortoPT174 papers
- University of CoimbraPT98 papers
- University of MinhoPT81 papers
- University of LisbonPT24 papers
- Centre National de la Recherche ScientifiqueFR22 papers
- Instituto Superior TécnicoPT22 papers
- UCLouvainBE13 papers
- Universidade Federal da BahiaBR13 papers
- Centro de Análise Matemática Geometria e Sistemas DinâmicosPT10 papers
- Pontifícia Universidade Católica do Rio de JaneiroBR10 papers
- Universidad de La LagunaES9 papers
- Universidade Federal do Rio de JaneiroBR9 papers
71 papers · 1 filter
Topological synchronisation or a simple attractor?
Theophile Caby, Michele Gianfelice, Benoit Saussol +1
A few recent papers introduced the concept of topological synchronisation. We refer in particular to \cite{TS}, where the theory was illustrated by means of a skew product system,…
Quenched decay of correlations for nonuniformly hyperbolic random maps with an ergodic driving system
José F. Alves, Wael Bahsoun, Marks Ruziboev +1
In this article we study random tower maps driven by an ergodic automorphism. We prove quenched exponential correlations decay for tower maps admitting exponential tails. Our techn…
Network Dynamics with Higher-Order Interactions: Coupled Cell Hypernetworks for Identical Cells and Synchrony
Manuela Aguiar, Christian Bick, Ana Dias
Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamic…
Synchrony in Gene Regulatory Networks
Manuela Aguiar, Ana Dias, Haibo Ruan
We consider two mathematical dynamical models of gene regulatory networks (GRNs) and obtain results on robust synchronization on these dynamical models based on the existing theore…
Persistent Strange attractors in 3D Polymatrix Replicators
Telmo Peixe, Alexandre A. Rodrigues
We introduce a one-parameter family of polymatrix replicators defined in a three-dimensional cube and study its bifurcations. For a given interval of parameters, this family exhibi…
Dissecting a resonance wedge on heteroclinic bifurcations
Alexandre A. P. Rodrigues
This article studies routes to chaos occurring within a resonance wedge for a 3-parametric family of differential equations acting on a 3-sphere. Our starting point is an autonomou…
Thermodynamic formalism for random non-uniformly expanding maps
Manuel Stadlbauer, Shintaro Suzuki, Paulo Varandas
We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of…
Torus-breakdown near a Bykov attractor: a case study
Luísa Castro, Alexandre A. P. Rodrigues
There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. This paper reports numerical experiments performed f…
Classification of Networks with Asymmetric Inputs
Manuela Aguiar, Ana Dias, Pedro Soares
Coupled cell systems associated with a coupled cell network are determined by (smooth) vector fields that are consistent with the network structure. Here, we follow the formalisms…
Generic homeomorphisms have full metric mean dimension
Maria Carvalho, Fagner B. Rodrigues, Paulo Varandas
We prove that the upper metric mean dimension of -generic homeomorphisms, acting on a compact smooth boundaryless manifold with dimension greater than one, coincides with the…
Asymptotic stability of robust heteroclinic networks
Olga Podvigina, Sofia B. S. D. Castro, Isabel S. Labouriau
We provide conditions guaranteeing that certain classes of robust heteroclinic networks are asymptotically stable. We study the asymptotic stability of ac-networks --- robust heter…
Almost complete and equable heteroclinic networks
Peter Ashwin, Sofia Castro, Alexander Lohse
Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems wi…
Chaos near a reversible homoclinic bifocus
Pablo G. Barrientos, Artem Raibekas, Alexandre A. P. Rodrigues
We show that any neighborhood of a non-degenerate reversible bifocal homoclinic orbit contains chaotic suspended invariant sets on -symbols for all . This will be achie…
Equilibrium states for a class of skew-products
Maria Carvalho, Sebastián A. Pérez
We consider skew-products on , where is the two-sphere or the two-torus, which are partially hyperbolic and semi-conjugate to an Axiom A diffeomorphism. T…
Dynamical counterexamples regarding the Extremal Index and the mean of the limiting cluster size distribution
Miguel Abadi, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
The Extremal Index is a parameter that measures the intensity of clustering of rare events and is usually equal to the reciprocal of the mean of the limiting cluster size distribut…
Hénon-like families and blender-horseshoes at non-transverse heterodimensional cycles
Lorenzo J. Díaz, Sebastián A. Pérez
In dimension three and under certain regularity assumptions, we construct a renormalisation scheme at the heterodimensional tangency of a non-transverse heterodimensional cycle ass…
The Lifting Bifurcation Problem on Feed-Forward Networks
Pedro Soares
We consider feed-forward networks, that is, networks where cells can be divided into layers, such that every edge targeting a layer, excluding the first one, starts in the prior la…
Stability of a heteroclinic network and its cycles: a case study from Boussinesq convection
Olga Podvigina, Sofia B. S. D. Castro, Isabel S. Labouriau
This article is concerned with three heteroclinic cycles forming a heteroclinic network in . The stability of the cycles and of the network are studied. The cycles a…
Complete set of invariants for a Bykov attractor
Maria Carvalho, Alexandre A. P. Rodrigues
In this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The b…
Networks with asymmetric inputs: lattice of synchrony subspaces
Manuela A. D. Aguiar
We consider coupled cell networks with asymmetric inputs and study their lattice of synchrony subspaces. For the particular case of 1-input regular coupled cell networks we describ…
Projections of Patterns and Mode Interactions
Sofia B. S. D. Castro, Isabel S. Labouriau, Juliane F. Oliveira
We study solutions of bifurcation problems with periodic boundary conditions, with periods in an -dimensional lattice and their projection into -dimensional space through i…
On the conservative pasting lemma
Pedro Teixeira
Several perturbation tools are established in the volume preserving setting allowing for the pasting, extension, localized smoothing and local linearization of vector fields. The p…
Extreme Value Laws for dynamical systems with countable extremal sets
Davide Azevedo, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas +1
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of th…
On Takens' Last Problem: tangencies and time averages near heteroclinic networks
Isabel S. Labouriau, Alexandre A. P. Rodrigues
We obtain a structurally stable family of smooth ordinary differential equations exhibiting heteroclinic tangencies for a dense subset of parameters. We use this to find vector fie…