4 papers
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…