Related papers: A solvable two-dimensional swarmalator model
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
Time delay can have a significant impact on the properties of collective organization of active matter. In the previous paper [1], we discussed delay-induced breathing in a system of swarmalators - a model coupling particles' internal…
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…
We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
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…
We investigate the transition from incoherence to global collective motion in a three-dimensional swarming model of agents with helical trajectories, subject to noise and global coupling. Without noise this model was recently proposed as a…
Populations of heterogeneous, noisy oscillators on a two-dimensional lattice display short-range order. Here, we show that if the oscillators are allowed to actively move in space, the system undergoes instead a…
The Kuramoto model, which describes synchronization phenomena, is a system of ordinary differential equations on $N$-torus defined as coupled harmonic oscillators. The order parameter is often used to measure the degree of synchronization.…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks complications to the application of the self-consistent…
We consider systems that are well modelled as a networks that evolve in time, which we call {\it Moving Neighborhood Networks}. These models are relevant in studying cooperative behavior of swarms and other phenomena where emergent…
Recently, there has been significant advancement in the machine learning (ML) approach and its application to diverse systems ranging from complex to quantum systems. As one of such systems, a coupled-oscillators system exhibits intriguing…
It is known from both theory and experiments that introducing time delays into the communication network of mobile-agent swarms produces coherent rotational patterns. Often such spatio-temporal rotations can be bistable with other swarming…
Using a recently introduced linear reformulation of the Kuramoto model of self-synchronizing oscillator systems (arXiv:0704.1166), we study a new class of analytically solvable oscillator systems defined by a particular coupling scheme. We…
We investigate the emergence of synchronization in the second-order Kuramoto model with adaptive simplicial interactions on a globally connected network. This inertial Kuramoto framework describes systems, where oscillator frequencies…
The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped…
We propose a new kind of collective motion where swarms of simple agents are able to find and fix the solution of two-dimensional mazes. The model consists of active memoryless particles interacting exclusively via short-ranged perception…
We study a one-dimensional swarmalator model with inertia. Previous studies have focused almost exclusively on the overdamped limit. We find inertia introduces a new unsteady collective state in which the rainbow order parameters undergo…
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.…