Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Pérez Cervera, Alberto"'
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary differential
Externí odkaz:
http://arxiv.org/abs/2404.09046
Autor:
Houzelstein, Pierre, Thomas, Peter J., Lindner, Benjamin, Gutkin, Boris S., Pérez-Cervera, Alberto
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 debated. In this work, we propose a method to derive a self-contained stoch
Externí odkaz:
http://arxiv.org/abs/2402.02856
In this paper we analyse the phenomenon of the slow passage through a transcritical bifurcation with special emphasis in the maximal delay $z_d(\lambda,\varepsilon)$ as a function of the bifurcation parameter $\lambda$ and the singular parameter $\va
Externí odkaz:
http://arxiv.org/abs/2309.10119
Publikováno v:
PNAS 120(29): e2303222120 (2023)
Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations, limit-cycle sys
Externí odkaz:
http://arxiv.org/abs/2303.03198
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 eigenvalue with a least negative real part, of the backward Kolmogorov (or
Externí odkaz:
http://arxiv.org/abs/2105.11048
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). Inferring the macroscopic PRC and developing a systematic phase reduction th
Externí odkaz:
http://arxiv.org/abs/2102.09409
In 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, via efficient algorithms, to obtain a parame
Externí odkaz:
http://arxiv.org/abs/2004.03647
The 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 depends not only on the strengt
Externí odkaz:
http://arxiv.org/abs/1905.06038
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 limit cycle. In this paper we present a new approach to PRCs based on th
Externí odkaz:
http://arxiv.org/abs/1809.07318
Publikováno v:
In Communications in Nonlinear Science and Numerical Simulation January 2020 80
