24 citations · 70 across the 7 of their papers we have counts for
7 papers
A Universal Description of Stochastic Oscillators
Alberto Pérez-Cervera, Boris Gutkin, Peter J. Thomas +1
Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for exampl…
Isostables for stochastic oscillators
Alberto Pérez-Cervera, Benjamin Lindner, Peter J. Thomas
Thomas and Lindner (2014, Phys.Rev.Lett.) defined an asymptotic phase for stochastic oscillators as the angle in the complex plane made by the eigenfunction, having a complex eigen…
Adjoint Method for Macroscopic Phase-Resetting Curves of Generic Spiking Neural Networks
Gregory Dumont, Alberto Pérez-Cervera, Boris Gutkin
Brain rhythms emerge as a result of synchronization among interconnected spiking neurons. Key properties of such rhythms can be gleaned from the phase-resetting curve (PRC). Inferr…
Global phase-amplitude description of oscillatory dynamics via the parameterization method
Alberto Pérez-Cervera, Tere M. Seara, Gemma Huguet
In this paper we use the parameterization method to provide a complete description of the dynamics of an -dimensional oscillator beyond the classical phase reduction. The parame…
Phase-locked states in oscillating neural networks and their role in neural communication
Alberto Pérez-Cervera, Tere M. Seara, Gemma Huguet
The theory of communication through coherence (CTC) proposes that brain oscillations reflect changes in the excitability of neurons, and therefore the successful communication betw…
The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability
A. Pérez-Cervera, P. Ashwin, G. Huguet +2
We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter uncouples the system at . Using a normal form…
A geometric approach to Phase Response Curves and its numerical computation through the parameterization method
Alberto Pérez-Cervera, Tere M. Seara, Gemma Huguet
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 li…