相关论文: Phase-locked Patterns of the Kuramoto Model on 3-R…

Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods. These approaches offer a useful visual picture for understanding the complexity of…

The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto…

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…

Some mathematical models of synchronization, such as the Kuramoto model (1975) and its generalizations pioneered by Lohe (2009), are formulated as ordinary differential equations describing populations of particles on Lie groups with…

Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…

We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an…

We study fixed points of cellular automata with $N$ sites on random sparse graphs. In the large $N$ limit such models are known to exhibit phase transitions, from a ``frozen'' phase, where at most a finite number of sites fluctuate at long…

Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the modeling procedure. On one hand, this can offer a more…

A statistical mechanic study of the $XY$ model with nonlinear interaction is presented on bipartite sparse random graphs. The model properties are compared to those of the $p$-clock model, in which the planar continuous spins are…

A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…

For any network of identical Kuramoto oscillators with identical positive coupling, there is a critical connectivity above which the system is guaranteed to converge to the in-phase synchronous state, for almost all initial conditions. But…

There are numerous examples of studied real-world systems that can be described as dynamical systems characterized by individual phases and coupled in a network like structure. Within the framework of oscillatory models, much attention has…

We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…

Nonlinear wave formation and propagation on a complex network with excitable node dynamics is of fundamental interest in diverse fields in science and engineering. Here, we propose a new model of the Kuramoto type to study nonlinear wave…

The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units.…

We study the Kuramoto model (KM) of coupled phase oscillators on graphs approximating the Sierpinski gasket (SG). As the size of the graph tends to infinity, the limit points of the sequence of stable equilibria in the KM correspond to the…

We study adaptive network models in which coupling weights evolve on a fast time scale relative to the phase dynamics of the nodes. Using Geometric Singular Perturbation Theory (GSPT), we prove that, although the microscopic system is…

We study the generic non-equilibrium steady states in asymmetric exclusion processes on a closed network with bottlenecks. To this end we proposes and study closed simple networks with multiply-connected non-identical junctions. Depending…

We derive a two-layer multiplex Kuramoto model from weakly coupled Wilson-Cowan oscillators on a cortical network with inhibitory synaptic time delays. Depending on the coupling strength and a phase shift parameter, related to cerebral…

We present an approach which enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether…