Related papers: Global phase-amplitude description of oscillatory …
We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit…
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…
Gamma frequency oscillations (25-140 Hz), observed in the neural activities within many brain regions, have long been regarded as a physiological basis underlying many brain functions, such as memory and attention. Among numerous…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a simple…
In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale…
We formulate a renormalization group approach to a general nonlinear oscillator problem. The approach is based on the exact group law obeyed by solutions of the corresponding ordinary differential equation. We consider both the autonomous…
The periodic modulation of an oscillator's frequency can lead to so-called parametric oscillations at half the driving frequency, which display bistability between two states whose phases differ by \pi. Such phase-locking bistability is at…
Coupled, nonlinear oscillators are often studied in applied biology, physics, fluids, and many other disciplines. In this paper, we study a parametrically driven, coupled oscillator system where the individual oscillators are subjected to…
Multivariate oscillatory signals from complex systems often exhibit non-stationary dynamics and metastable regime structure, making dynamical interpretation challenging. We introduce a ``dynamical microscope'' framework that converts…
In this paper we explore challenges in developing a topological framework in which machine learning can be used to robustly characterize global dynamics. Specifically, we focus on learning a useful discretization of the phase space of a…
For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…
The analysis of the fully three-dimensional and time-varying polarization characteristics of a modulated trivariate, or three-component, oscillation is addressed. The use of the analytic operator enables the instantaneous three-dimensional…
The describing function method is a useful tool for the qualitative analysis of limit cycles in the stability analysis of nonlinear systems. This method is inherently approximate; therefore, it should be used for a fast qualitative analysis…
Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show that application of the methods of…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…
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…