38 citations · 131 across the 30 of their papers we have counts for
36 papers
The Bosch and Simó conjecture on the Shilnikov-Hopf bifurcation
Alexandre A. P. Rodrigues
We provide a rigorous mathematical proof of the Bosch-Simó conjecture ( M. Bosch, C. Simó (1993), Physica D, 217--229) regarding the abundance of strange attractors in the unfoldin…
Three-dimensional horseshoes near an unfolding of a Hopf-Hopf singularity
Santiago Ibáñez, Alexandre A. P. Rodrigues
Motivated by a certain type of unfolding of a Hopf-Hopf singularity, we consider a one-parameter family of --vector fields in whose flows exhib…
On the dynamics of rotating rank-one strange attractors families
Alexandre A. P. Rodrigues, Bruno F. Gonçalves
In this article, we study a two-parameter family of rotating rank-one maps defined on , with , whose dynamics is charact…
Transitions of bifurcation diagrams of a forced heteroclinic cycle
Isabel S. Labouriau, Alexandre A. P Rodrigues
A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of map…
High frequency forcing of an attracting heteroclinic cycle
Isabel S. Labouriau, Alexandre A. P. Rodrigues
This article is concerned with the effect of time-periodic forcing on a vector field exhibiting an attracting heteroclinic network. We show that as the forcing frequency tends to i…
Differential equations with pulses: existence and stability of periodic solutions
Alexandre A. P. Rodrigues
We consider generic differential equations in with a finite number of hyperbolic equilibria, which are subject to --periodic instantaneous perturbative pulses ($ω>0…
SIR model with vaccination: bifurcation analysis
João P. S. Maurício de Carvalho, Alexandre A. Rodrigues
There are few adapted SIR models in the literature that combine vaccination and logistic growth. In this article, we study bifurcations of a SIR model where the class of Susceptibl…
Abundance of infinite switching
Alexandre A. Rodrigues, Maria Luisa Castro
In this article, we describe a class of vector fields exhibiting abundant switching} near a network: for every neighbourhood of the network and every infinite admissible path, the…
Stability of heteroclinic cycles: a new approach
Telmo Peixe, Alexandre A. Rodrigues
This paper analyses the stability of cycles within a heteroclinic network lying in a three-dimensional manifold formed by six cycles, for a one-parameter model developed in the con…
Rank-one strange attractors versus Heteroclinic tangles
Alexandre A. P. Rodrigues
We present a mechanism for the emergence of strange attractors (observable chaos) in a two-parameter periodically-perturbed family of differential equations on the plane. The two p…
"Large" strange attractors in the unfolding of a heteroclinic attractor
Alexandre A. P. Rodrigues
In this paper we present a mechanism for the emergence of strange attractors in a one-parameter family of differential equations acting on a 3-dimensional sphere. When the paramete…
Periodic forcing of a heteroclinic network
Isabel S. Labouriau, Alexandre A. P. Rodrigues
We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential e…
Strange attractors in a dynamical system inspired by a seasonally forced SIR model
João P. S. Maurício de Carvalho, Alexandre A. Rodrigues
We analyze a multiparameter periodically-forced dynamical system inspired in the SIR endemic model. We show that the condition on the \emph{basic reproduction number} $\mathcal{R}_…
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…
Abundance of strange attractors near an attracting periodically-perturbed network
Alexandre A. P. Rodrigues
We study the dynamics of the periodically-forced May-Leonard system. We extend previous results on the field and we identify different dynamical regimes depending on the strength o…
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…
Unfolding a Bykov attractor: from an attracting torus to strange attractors
Alexandre A. P. Rodrigues
In this paper we present a comprehensive mechanism for the emergence of strange attractors in a two-parametric family of differential equations acting on a three-dimensional sphere…
Moduli of stability for heteroclinic cycles of periodic solutions
Maria Carvalho, Alexander Lohse, Alexandre Rodrigues
We consider vector fields in the three dimensional sphere with an attracting heteroclinic cycle between two periodic hyperbolic solutions with real Floquet multipliers. The p…
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…
Bifurcations from an attracting heteroclinic cycle under periodic forcing
Isabel S. Labouriau, Alexandre A. P. Rodrigues
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attrac…
Strange attractors and non wandering domains near a homoclinic cycle to a bifocus
Alexandre A. P. Rodrigues
In this paper, we explore the three-dimensional chaotic set near a homoclinic cycle to a hyperbolic bifocus at which the vector field has negative divergence. If the invariant mani…
The role of the saddle-foci on the structure of a Bykov attracting set
Mario Bessa, Maria Carvalho, Alexandre A. P. Rodrigues
We consider a one-parameter family of symmetric vector fields on the three-dimensional sphere whose flows exhibit a h…
Attractors in complex networks
Alexandre A. P. Rodrigues
In the framework of the generalized Lotka Volterra model, solutions representing multispecies sequencial competition can be predictable with high probability. In this paper, we sho…