Related papers: Augmented Phase Reduction for Periodic Orbits Near…

We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a…

Building oscillator based computing systems with emerging nano-device technologies has become a promising solution for unconventional computing tasks like computer vision and pattern recognition. However, simulation and analysis of these…

We present an analytical calculation of periodic orbits in the homogeneous quartic oscillator potential. Exploiting the properties of the periodic Lam{\'e} functions that describe the orbits bifurcated from the fundamental linear orbit in…

Periodic orbits are fundamental to understand the dynamics of nonlinear systems. In this work, we focus on two aspects of interest regarding periodic orbits, in the context of a dissipative mapping, derived from a prototype model of a…

Given the high dimensionality and underlying complexity of many oscillatory dynamical systems, phase reduction is often an imperative first step in control applications where oscillation timing and entrainment are of interest.…

Stochastic oscillations are ubiquitous in many systems. For deterministic systems, the oscillator's phase has been widely used as an effective one-dimensional description of a higher dimensional dynamics, particularly for driven or coupled…

Oscillatory reconnection is a time-dependent magnetic reconnection mechanism that naturally produces periodic outputs from aperiodic drivers. This paper aims to quantify and measure the periodic nature of oscillatory reconnection for the…

Spontaneous oscillations induced by time delays are observed in many real-world systems. Phase reduction theory for limit-cycle oscillators described by delay-differential equations (DDEs) has been developed to analyze their synchronization…

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…

Phase reduction is a powerful technique in the study of nonlinear oscillatory systems. Under certain assumptions, it allows us to describe each multidimensional oscillator by a single phase variable, giving rise to simple phase models such…

Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…

Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…

We investigate the evolution of families of periodic orbits in a bisymmetrical potential made up of a two-dimensional harmonic oscillator with only one quartic perturbing term, in a number of resonant cases. Our main objective is to compute…

We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the…

This is a comment on a recent paper by Yoshimura and Arai [Phys. Rev. Lett. 101, 154101 (2008)] on phase reduction of noisy limit-cycle oscillators, in which the authors claimed that the conventional phase stochastic differential equation…

Higher precision efficient computation of period 1 relaxation oscillations of strongly nonlinear and singularly perturbed Rayleigh equations with external periodic forcing is presented. The computations are performed in the context of…

Analytical solution of the homoclinic orbit of a two dimensional system of differential equations that describes the hamiltonian part of the slow flow of a three degree of freedom dissipative system of linear coupled oscillators with an…

We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…

The phase-amplitude framework extends the classical phase reduction method by incorporating amplitude coordinates (or isostables) to describe transient dynamics transverse to the limit cycle in a simplified form. While the full set of…

We review the state space decomposition techniques for the assessment of the noise properties of autonomous oscillators, a topic of great practical and theoretical importance for many applications in many different fields, from electronics,…