4 papers
Efficient Numerical Algorithms for Phase-Amplitude Reduction on the Slow Attracting Manifold of Limit cycles
David Reyner-Parra, Alberto Pérez-Cervera, Gemma Huguet
The phase-amplitude framework extends the classical phase reduction method by incorporating amplitude coordinates (or isostables) to describe transient dynamics transverse to the l…
Phase-Amplitude Description of Stochastic Oscillators: A Parameterization Method Approach
Alberto Pérez-Cervera, Benjamin Lindner, Peter J. Thomas
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables i…
Generalized dynamical phase reduction for stochastic oscillators
Pierre Houzelstein, Peter J. Thomas, Benjamin Lindner +2
Phase reduction is an important tool for studying coupled and driven oscillators. The question of how to generalize phase reduction to stochastic oscillators remains actively debat…
Slow passage through a transcritical bifurcation in piecewise linear differential systems: canard explosion and enhanced delay
Alberto Pérez-Cervera, Antonio E. Teruel
In 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…