Related papers: Nonlinear waves on circle networks with excitable …
Collective oscillations and patterns of synchrony have long fascinated researchers in the applied sciences, particularly due to their far-reaching importance in chemistry, physics, and biology. The Kuramoto model has emerged as a…
This work considers an extension of the Kuramoto model with run-and-tumble dynamics -- a type of self-propelled motion. The difference between the extended and the original model is that in the extended version angular velocity of…
We prove the existence and uniqueness of a family of travelling waves in a degenerate (or singular) quasilinear parabolic problem that may be regarded as a generalization of the semilinear Fisher-Kolmogorov-Petrovski-Piscounov equation for…
We study radial waves in (2+1)-dimensional noncommutative scalar field theory, using operatorial methods. The waves propagate along a discrete radial coordinate and are described by finite series deformations of Bessel-type functions. At…
We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstrate that time delays shape the spectrum of a matrix…
The one-dimension Russo--Smereka kinetic equation describing the propagation of nonlinear concentration waves in a rarefied bubbly fluid is considered. Reductions of the model to finite component systems are derived. Stability of the bubbly…
In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…
In graphene, where the electron-electron scattering is dominant, electrons collectively act as a fluid. This hydrodynamic behaviour of charge carriers leads to exciting nonlinear phenomena such as solitary waves and shocks, among others. In…
Nonlinear electromagnetic waves with superluminal phase velocity can propagate in the winds around isolated pulsars, and around some pulsars in binary systems. Using a short-wavelength approximation, we find and analyze an integrable system…
We consider a discrete model that describes a linear chain of particles coupled to a single-site defect with instantaneous Kerr nonlinearity. We show that this model can be regarded as a nonlinear generalization of the familiar…
Spiral waves arise in many biological, chemical, and physiological systems. The kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane. For this model, there appeared some results in the…
We study synchronization of Kuramoto oscillators in strongly modular networks in which the structure of the network inside each community is averaged. We find that the dynamics of the interacting communities can be described as an ensemble…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
The number $\mathcal{N}$ of stable fixed points of locally coupled Kuramoto models depends on the topology of the network on which the model is defined. It has been shown that cycles in meshed networks play a crucial role in determining…
We study the localization properties of disordered d-wave superconductors by means of the fermionic replica trick method. We derive the effective non-linear sigma-model describing the diffusive modes related to spin transport which we…
Phase balanced states are a highly under-explored class of solutions of the Kuramoto model and other coupled oscillator models on networks. So far, coupled oscillator research focused on phase synchronized solutions. Yet, global constraints…
In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is…
The aim of this paper is to investigate complex dynamic networks which can model high-voltage power grids with renewable, fluctuating energy sources. For this purpose we use the Kuramoto model with inertia to model the network of power…
We study the Kuramoto model (KM) having random natural frequencies and defined on uniform graphs that may be complete, random dense or random sparse. The natural frequencies are assumed to be independent and identically distributed on a…
A general theory of edge spin wave excitations in semi-infinite and finite periodic arrays of magnetic nanodots existing in a spatially uniform magnetization ground state is developed. The theory is formulated using a formalism of…