Hopf-Zero singularities truly unfold chaos

I Baldomá, S Ibáñez, TM Seara - Communications in Nonlinear Science …, 2020‏ - Elsevier
We provide conditions to guarantee the occurrence of Shilnikov bifurcations in analytic
unfoldings of some Hopf-Zero singularities through a beyond all order phenomenon: the …

On the dynamics near a homoclinic network to a bifocus: switching and horseshoes

S Ibánez, A Rodrigues - International Journal of Bifurcation and …, 2015‏ - World Scientific
We study a homoclinic network associated to a nonresonant hyperbolic bifocus. It is proved
that on combining rotation with a nondegeneracy condition concerning the intersection of …

[HTML][HTML] Connecting chaotic regions in the Coupled Brusselator System

F Drubi, A Mayora-Cebollero… - Chaos, Solitons & …, 2023‏ - Elsevier
A family of vector fields describing two Brusselators linearly coupled by diffusion is
considered. This model is a well-known example of how identical oscillatory systems can be …

[HTML][HTML] Using Lin's method to solve Bykov's problems

J Knobloch, JSW Lamb, KN Webster - Journal of Differential Equations, 2014‏ - Elsevier
We consider nonwandering dynamics near heteroclinic cycles between two hyperbolic
equilibria. The constituting heteroclinic connections are assumed to be such that one of …

[HTML][HTML] Invariant manifolds in a reversible Hamiltonian system: the tentacle-like geometry

PS Casas, F Drubi, S Ibáñez - Communications in Nonlinear Science and …, 2024‏ - Elsevier
We study a one-parameter family of time-reversible Hamiltonian vector fields in R 4, which
has received great attention in the literature. On the one hand, it is due to the role it plays in …

Nilpotent singularities and chaos: Tritrophic food chains

F Drubi, S Ibáñez, P Pilarczyk - Chaos, Solitons & Fractals, 2021‏ - Elsevier
Local bifurcation theory is used to prove the existence of chaotic dynamics in two well-
known models of tritrophic food chains. To the best of our knowledge, the simplest technique …

Chaotic motion and singularity structures of front solutions in multi-component FitzHugh-Nagumo-type systems

M Chirilus-Bruckner, P van Heijster… - arxiv preprint arxiv …, 2024‏ - arxiv.org
We study the dynamics of front solutions in a certain class of multi-component reaction-
diffusion systems, where one fast component governed by an Allen-Cahn equation is weakly …

Robust cycles unfolding from conservative bifocal homoclinic orbits

PG Barrientos, S Ibáñez, JÁ Rodríguez - Dynamical Systems, 2016‏ - Taylor & Francis
We prove that suspended robust heterodimensional cycles and suspended robust
homoclinic tangencies can be found arbitrarily close to any non-degenerate bifocal …

[HTML][HTML] Strange attractors and wandering domains near a homoclinic cycle to a bifocus

AAP Rodrigues - Journal of Differential Equations, 2020‏ - Elsevier
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 …

Emergence of Strange Attractors from Singularities

JA Rodríguez - Regular and Chaotic Dynamics, 2023‏ - Springer
This paper is a summary of results that prove the abundance of one-dimensional strange
attractors near a Shil'nikov configuration, as well as the presence of these configurations in …