Related papers: Periodic orbits in the Ott-Antonsen manifold
Synchronization of weakly-coupled non-linear oscillators is a ubiquitous phenomenon that has been observed across the natural sciences. We study the dynamics of optomechanical arrays - networks of mechanically compliant structures that…
We show that amplitude-mediated phase chimeras and amplitude chimeras can occur in the same network of nonlocally coupled identical oscillators. These are two different partial synchronization patterns, where spatially coherent domains…
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…
Collective behaviors of populations of coupled oscillators have attracted much attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynam- ical mechanism of collective…
The Ott-Antonsen ansatz shows that, for certain classes of distribution of the natural frequencies in systems of $N$ globally coupled Kuramoto oscillators, the dynamics of the order parameter, in the limit $N\to \infty$, evolves, under…
Phase reduction is a dimensionality reduction scheme to describe the dynamics of nonlinear oscillators with a single phase variable. While it is crucial in synchronization analysis of coupled oscillators, analytical results are limited to…
Understanding the global dynamical behaviour of a network of coupled oscillators has been a topic of immense research in many fields of science and engineering. Various factors govern the resulting dynamical behaviour of such networks,…
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…
Low-dimensional reduction theories, such as the Ott-Antonsen ansatz, have played a crucial role in the study of populations of globally coupled phase oscillators. However, most of these theories are applicable only to models in which the…
We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from…
We propose a robust universal approach to identify multiple dynamical states, including stationary and travelling chimera states based on an adaptive coherence measure. Our approach allows automatic disambiguation of synchronized clusters,…
We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the…
In a network of coupled oscillators, a symmetry-broken dynamical state characterized by the coexistence of coherent and incoherent parts can spontaneously form. It is known as a chimera state. We study chimera states in a network consisting…
Partial synchronization is characteristic phase dynamics of coupled oscillators on various natural and artificial networks, which can remain undetected due to the complexity of the systems. With an analogy between pairwise asynchrony of…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…
Out-of-Time-Order Correlators (OTOCs) quantify quantum information scrambling, but their connection to localized phase-space structures, such as chemical transition states, requires formal development. We derive a leading-order…
We present an analytical description for the collective dynamics of oscillator ensembles with higher-order coupling encoded by simplicial structure, which serves as an illustrative and insightful paradigm for brain function and information…
We analyze the synchronization dynamics of phase oscillators far from the synchronization manifold, including the onset of synchronization on scale-free networks with low and high clustering coefficients. We use normal coordinates and…
Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between…