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The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability
(2019-12-01)
Article.
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Article.
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We study the dynamics arising when two identical oscillators are coupled near a Hopfbifurcation where we assume a parameter uncouples the system at = 0. Using anormal form forN= 2 identical systems undergoing Hopf bifurcation, ...
Regularization around a generic codimension one fold-fold singularity
(2018-09-05)
Article.
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Article.
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This paper is devoted to study the generic fold-fold singularity of Filippov systems on the plane, its unfoldings and its Sotomayor–Teixeira regularization. We work with general Filippov systems and provide the bifurcation ...
Chaos in the hysteretic grazing-sliding codimension-one saddle-node bifurcation of piecewise dynamical systems
(UP4, Institute of Sciences, S.L., 2017)
Comunicació de congrés.
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Comunicació de congrés.
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We present two ways of regularizing a parameter family of piecewise smooth dynamical systems undergoing a grazing- sliding bifurcation. We use the Sotomayor-Teixeira regularization and prove that the bifurcation is a ...
Computation of invariant curves in the analysis of periodically forced neural oscillators
(Springer, 2018)
Capítol de llibre.
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Capítol de llibre.
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Background oscillations, reflecting the excitability of neurons, are ubiq- uitous in the brain. Some studies have conjectured that when spikes sent by one population reach the other population in the peaks of excitability, ...
A unified approach to explain contrary effects of hysteresis and smoothing in nonsmooth systems
(2017-09-01)
Article.
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Article.
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Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should the dynamics be given ...
Instability of high dimensional Hamiltonian systems: Multiple resonances do not impede diffusion
(2016-05-14)
Article.
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Article.
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We consider models given by Hamiltonians of the form View the MathML sourceH(I,f,p,q,t;e)=h(I)+¿j=1n±(12pj2+Vj(qj))+eQ(I,f,p,q,t;e) Turn MathJax on where I¿I¿Rd,f¿TdI¿I¿Rd,f¿Td, p,q¿Rnp,q¿Rn, t¿T1t¿T1. These are higher ...
A general mechanism of diffusion in hamiltonian systems: qualitative results
(2019-01-01)
Article.
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Article.
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We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach is based on following the “outer dynamics” along homoclinic orbits to a ...
Study of periodic orbits in periodic perturbations of planar reversible Filippov systems having a twofold cycle
(2020-01-01)
Article.
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Article.
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We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed ...
On the asymptotic wavenumber of spiral waves in lambda - omega systems
(2016-01-01)
Article.
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Article.
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In this paper we consider spiral wave solutions of a general class of $\lambda -\omega $ systems with a small twist parameter q and we prove that the asymptotic wavenumber of the spirals is a ${{\mathcal{C}}^{\infty}}$ ...
Phase-locked states in oscillating neural networks and their role in neural communication
(2020-01-01)
Article.
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Article.
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The theory of communication through coherence (CTC) proposes that brain oscillations reflect changes in the excitability of neurons, and therefore the successful communication between two oscillating neural populations ...