Related papers: Direct extraction of phase dynamics from fluctuati…
An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be…
Objective. We identify two linked problems related to estimating the phase of the alpha rhythm when the signal after a specific event is unknown (real-time case), or corrupted (offline analysis). We propose methods to estimate the phase…
We show that the numerical method based on the off-equilibrium fluctuation-dissipation relation does work and is very useful and powerful in the study of disordered systems which show a very slow dynamics. We have verified that it gives the…
Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the…
We introduce a variational method for analyzing limit cycle oscillators in $\mathbb{R}^d$ driven by Gaussian noise. This allows us to derive exact stochastic differential equations (SDEs) for the amplitude and phase of the solution, which…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
We analyze the stochastic response of a finite set of globally coupled noisy bistable units driven by rather weak time-periodic forces. We focus on the stochastic resonance and phase frequency synchronization of the collective variable,…
Understanding how systems evolve over time often requires discovering the differential equations that govern their behavior. Automatically learning these equations from experimental data is challenging when the data are noisy or limited,…
We present an approach for reconstructing networks of pulse-coupled neuron-like oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases…
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…
We compute the joint large deviation rate functional in the limit of large time for the current flowing through the edges of a finite graph on which a boundary-driven system of stochastic particles evolves with zero-range dynamics.This…
We apply the phase-reduction analysis to examine synchronization properties of periodic fluid flows. The dynamics of unsteady flows are described in terms of the phase dynamics reducing the high-dimensional fluid flow to its single scalar…
Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical…
Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve…
We propose a method for designing two-dimensional limit-cycle oscillators with prescribed periodic trajectories and phase response properties based on the phase reduction theory, which gives a concise description of weakly-perturbed…
The extraction of oscillatory components and their properties from different time-frequency representations, such as windowed Fourier transform and wavelet transform, is an important topic in signal processing. The first step in this…
We point out that the phase reduction of stochastic limit cycle oscillators has been done incorrectly in the literature. We present a correct phase reduction method for oscillators driven by weak external white Gaussian noises. Numerical…
We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely…
We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal…
Spatiotemporal dynamics is central to a wide range of applications from climatology, computer vision to neural sciences. From temporal observations taken on a high-dimensional vector of spatial locations, we seek to derive knowledge about…