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…
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 th…
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…