Now showing items 1-20 of 21

• #### A computational and geometric approach to phase resetting curves and surfaces ﻿

(2009)
Article
Open Access
• #### A geometric approach to phase response curves and its numerical computation through the parameterization method ﻿

(2019-01-01)
Article
Open Access
The phase response curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the limit cycle. In this paper, we present a new ...
• #### A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems ﻿

(2010-07)
External research report
Open Access
In this paper we consider a representative a priori unstable Hamiltonian system with 2 + 1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem. Amer. ...
• #### A geometric mechanism of diffusion: rigorous verification in a priori unstable Hamiltonian systems ﻿

(2011-03-01)
Article
Restricted access - publisher's policy
In this paper we consider a representative a priori unstable Hamiltonian system with 2 + 1/2 degrees of freedom and we apply the geometric mechanism for diffusion introduced in [A. Delshams, R. de la Llave, T.M. Seara, ...
• #### Computation of invariant curves in the analysis of periodically forced neural oscillators ﻿

(Springer, 2018)
Part of book or chapter of book
Open Access
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, ...
• #### Computation of limit cycles and their isochrons: Fast algorithms and their convergence ﻿

(2013)
Article
Restricted access - publisher's policy
We present efficient algorithms to compute limit cycles and their isochrons (i.e., the sets of points with the same asymptotic phase) for planar vector fields. We formulate a functional equation for the parameterization ...
• #### Dones i Matemàtiques ﻿

(2015-03-11)
Audiovisual
Open Access
L'objectiu d'aquesta taula rodona és abordar la situació de les dones en el camp de les matemàtiques. Tot i que actualment l'activitat matemàtica de les dones és més gran que mai, encara són poques les dones que es dediquen ...
• #### Effects of thermoregulation on human sleep patterns: A mathematical model of sleep-wake cycles with REM-NREM subcircuit ﻿

(2015)
Part of book or chapter of book
Open Access
In this paper we construct a mathematical model of human sleep/wake regulation with thermoregulation and temperature e ects. Simulations of this model show features previously presented in experimental data such as elongation ...
• #### Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems ﻿

(2008-12-08)
Article
Open Access
In the present paper we consider the case of a general $\cont{r+2}$ perturbation, for $r$ large enough, of an a priori unstable Hamiltonian system of $2+1/2$ degrees of freedom, and we provide explicit conditions on it, ...
• #### Global phase-amplitude description of oscillatory dynamics via the parameterization method ﻿

(Institute of Physics (IOP), 2020-08-01)
Article
Open Access
In this paper, we use the parameterization method to provide a complete description of the dynamics of an n-dimensional oscillator beyond the classical phase reduction. The parameterization method allows us, via efficient ...
• #### Gluing and grazing bifurcations in periodically forced 2-dimensional integrate-and-fire models ﻿

(2019-05-01)
Article
Open Access
In this work we consider a general class of 2-dimensional hybrid systems. Assuming that the system possesses an attracting equilibrium point, we show that, when periodically driven with a square-wave pulse, the system ...
• #### Modeling the long term effects of thermoregulation on human sleep ﻿

(2020-05-21)
Article
Open Access
The connection between human sleep and energy exertion has long been regarded as part of the reasoning for the need to sleep. A recent theory proposes that during REM sleep, energy utilized for thermoregulation is diverted ...
• #### Neuroprotective Role of Gap Junctions in a Neuron Astrocyte Network Model ﻿

(2016-07-26)
Article
Open Access
A detailed biophysical model for a neuron/astrocyte network is developed to explore mechanisms responsible for the initiation and propagation of cortical spreading depolarizations and the role of astrocytes in maintaining ...
• #### Noise and adaptation in multistable perception: noise drives when to switch, adaptation determines percept choice. ﻿

(2014-03-13)
Article
Open Access
We study the dynamics of perceptual switching in ambiguous visual scenes that admit more than two interpretations/percepts to gain insight into the dynamics of perceptual multistability and its underlying neural mechanisms. ...
• #### Phase-amplitude response functions for transient-state stimuli ﻿

(2013-08)
Article
Open Access
The phase response curve (PRC) is a powerful tool to study the effect of a perturbation on the phase of an oscillator, assuming that all the dynamics can be explained by the phase variable. However, factors like the rate ...
• #### Phase-locked states in oscillating neural networks and their role in neural communication ﻿

(2020-01-01)
Article
Open Access
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 ...
• #### Phasic firing and coincidence detection by subthreshold negative feedback: divisive or subtractive or, better, both ﻿

(2017-02-02)
Article
Open Access
Phasic neurons typically fire only for a fast-rising input, say at the onset of a step current, but not for steady or slow inputs, a property associated with type III excitability. Phasic neurons can show extraordinary ...
• #### Quasiperiodic perturbations of heteroclinic attractor networks ﻿

(Institute of Physics (IOP), 2018-10-01)
Article
Open Access
We consider heteroclinic attractor networks motivated by models of competition between neural populations during binocular rivalry. We show that gamma distributions of dominance times observed experimentally in binocular ...
• #### SISTEMES DINÀMICS ﻿

(Universitat Politècnica de Catalunya, 2019-01-18)
Exam