Browsing by Author "Pérez Cervera, Alberto"
Now showing items 1-7 of 7
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A geometric approach to phase response curves and its numerical computation through the parameterization method
(2019-01-01)
Article
Open AccessThe 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 ... -
Computation of invariant curves in the analysis of periodically forced neural oscillators
(Springer, 2018)
Part of book or chapter of book
Open AccessBackground 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, ... -
Global phase-amplitude description of oscillatory dynamics via the parameterization method
(Institute of Physics (IOP), 2020-08-01)
Article
Open AccessIn 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 ... -
On the role of oscillatory dynamics in neural communication
(Universitat Politècnica de Catalunya, 2019-04-04)
Doctoral thesis
Open AccessIn this Thesis we consider problems concerning brain oscillations generated across the interaction between excitatory (E) and inhibitory (I) cells. We explore how two neuronal groups with underlying oscillatory activity ... -
Phase-locked states in oscillating neural networks and their role in neural communication
(2020-01-01)
Article
Open AccessThe 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 ... -
Slow passage through a transcritical bifurcation in piecewise linear differential systems: canard explosion and enhanced delay
(Elsevier, 2024-03-03)
Article
Restricted access - publisher's policyIn this paper we analyse the phenomenon of the slow passage through a transcritical bifurcation with special emphasis in the maximal delay ¿ as a function of the bifurcation parameter and the singular parameter ¿ . We ... -
The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability
(2019-12-01)
Article
Open AccessWe 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, ...
