Related papers: Exactly solvable phase oscillator models with sync…
We generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
We show the first solvable chaotic synchronization model of unidirectionally coupled dynamical systems. We establish a new interpretation of the conditional Lyapunov exponent that characterizes chaotic synchronization completely. Moreover,…
A new type of nonlinear time series analysis is introduced, based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates. A canonical choice of the polar axis and a related implicit…
In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the…
During the past decades, the question of existence and properties of a random attractor of a random dynamical system generated by an S(P)DE has received considerable attention, for example by the work of Gess and R\"ockner. Recently some…
We investigate the existence of an optimal interplay between the natural frequencies of a group chaotic oscillators and the topological properties of the network they are embedded in. We identify the conditions for achieving phase…
Synchronization of forced reactively coupled van der Pol oscillators is investigated in the phase approximation. We discuss essential features of the reactive coupling. Bifurcation mechanisms for the destruction of complete synchronization…
The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates…
Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the…
We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian…
We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between…
Schroedinger bound-state problem in D dimensions is considered for a set of central polynomial potentials (containing 2q coupling constants). Its polynomial (harmonic-oscillator-like, quasi-exact, terminating) bound-state solutions of…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoherent oscillations. The recently-introduced notion of a weak…
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 study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected…
We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…
Empirically defining some constant probabilistic orbits of f(x) and g(x) iterated high-order functions, the stability of these functions in possible entangled interaction dynamics of the environment through its orbit's connectivity (open…
A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and…