Related papers: Direct extraction of phase dynamics from fluctuati…

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to…

Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the…

We propose a network of oscillators to retrieve given patterns in which the oscillators keep a fixed phase relationship with one another. In this description, the phase and the amplitude of the oscillators can be regarded as the timing and…

The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…

A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can…

We present a novel method of reconstructing the phase-amplitude dynamics directly from measured electrophysiological signals to estimate the coupling between brain regions. For this purpose, we use the recent advances in the field of…

In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In…

Complex, oscillatory data arises from a large variety of biological, physical, and social systems. However, the inherent oscillation and ubiquitous noise pose great challenges to current methodology such as linear and nonlinear time series…

Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…

The phase reduction method is a dimension reduction method for weakly driven limit-cycle oscillators, which has played an important role in the theoretical analysis of synchro- nization phenomena. Recently, we proposed a generalization of…

This paper introduces a novel approach for modelling time-varying connectivity in neuroimaging data, focusing on the slow fluctuations in synaptic efficacy that mediate neuronal dynamics. Building on the framework of Dynamic Causal…

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely…

The synchronization analysis of limit-cycle oscillators is prevalent in many fields, including physics, chemistry, and life sciences. It relies on the phase calculation that utilizes measurements. However, the synchronization of…

We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is…

The paper describes the application of some numerical techniques to analyze and to characterize the observed dynamical behaviour of fluidized bed systems. The preliminary results showed clearly that the dynamics of the considered process…

Phase reduction is a well-established technique used to analyze the timing of oscillations in response to weak external inputs. In the preceding decades, a wide variety of results have been obtained for weakly perturbed oscillators that…

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…

Whisking is a rhythmic and adaptive behavior that rodents use to probe and interact with their environment, and the frequency of movement reflects both sensorimotor processing and internal brain states. A robust and traditional method of…

We consider the weakly asymmetric simple exclusion process on a ring, driven out of equilibrium by tilting the dynamics so as to enforce a macroscopic current of particles on a large time interval. In this current-biased dynamics, the tilt…

This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…