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Hopf-Zero singularities truly unfold chaos
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 …
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
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 …
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 …
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
We consider nonwandering dynamics near heteroclinic cycles between two hyperbolic
equilibria. The constituting heteroclinic connections are assumed to be such that one of …
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 …
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
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 …
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
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 …
diffusion systems, where one fast component governed by an Allen-Cahn equation is weakly …
Robust cycles unfolding from conservative bifocal homoclinic orbits
We prove that suspended robust heterodimensional cycles and suspended robust
homoclinic tangencies can be found arbitrarily close to any non-degenerate bifocal …
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
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 …
hyperbolic bifocus at which the vector field has negative divergence. If the invariant …
Emergence of Strange Attractors from Singularities
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 …
attractors near a Shil'nikov configuration, as well as the presence of these configurations in …