Related papers: Phase Synchronization and Polarization Ordering of…
We study collective behavior of locally-coupled limit-cycle oscillators with scattered intrinsic frequencies on $d$-dimensional lattices. A linear analysis shows that the system should be always desynchronized up to $d=4$. On the other…
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…
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…
Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units,…
Phase synchronization refers to a kind of collective phenomenon that the phase difference between two or more systems is locked, and it has widely been investigated between systems with the identical physical properties, such as the…
Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the…
We make a short review about the synchronization in coupled phase oscillator models. Next, we study the common-noise-induced synchronization among active rotators. At an intermediate noise strength, the noise-induced synchronization takes…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
Synchronization among rhythmic elements is modeled by coupled phase-oscillators each of which has the so-called natural frequency. A symmetric natural frequency distribution induces a continuous or discontinuous synchronization transition…
We develop a linear response theory by computing the asymptotic value of the order parameter from the linearized equation of continuity around the nonsynchronized reference state using the Laplace transform in time. The proposed theory is…
In this paper we consider an approach, which allows researching a processes of order-disorder transition in various systems (with any distribution of the exchange integrals signs) in the frame of Ising model. A new order parameters, which…
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the…
We show that a lattice of phase oscillators with random natural frequencies, described by a generalization of the nearest-neighbor Kuramoto model with an additional cosine coupling term, undergoes a phase transition from a desynchronized to…
Synchronization in a lattice of a finite population of phase oscillators with algebraically decaying, non-normalized coupling is studied by numerical simulations. A critical level of decay is found, below which full locking takes place if…
An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be…
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
A coupled-phase oscillator model where each oscillator has an angular velocity that varies due to the interaction with other oscillators is studied. This model is proposed to deepen the understanding of the relationship between the…
The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling. The population is described by a Fokker-Planck equation…
An oscillatory system can have clockwise and anticlockwise senses of rotation. We propose a general rule how to obtain counter-rotating oscillators from the definition of a dynamical system and then investigate synchronization. A type of…