Phase synchronization in the two-dimensional Kuramoto model: Vortices and duality

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Mrinal Sarkar ◽  
Neelima Gupte
Keyword(s):  
Phase Synchronization ◽  
Kuramoto Model ◽  
Two Dimensional

scholarly journals Vortices and the entrainment transition in the two-dimensional Kuramoto model

2010 ◽  
Vol 82 (3) ◽  
Author(s):  
Tony E. Lee ◽  
Heywood Tam ◽  
G. Refael ◽  
Jeffrey L. Rogers ◽  
M. C. Cross
Keyword(s):  
Kuramoto Model ◽  
Two Dimensional

Remarks on the complete synchronization for the Kuramoto model with frustrations

2018 ◽  
Vol 16 (04) ◽  
pp. 525-563 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Hwa Kil Kim ◽  
Jinyeong Park
Keyword(s):  
Phase Synchronization ◽  
Kuramoto Model ◽  
Prototype Model ◽  
Frequency Synchronization ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Kuramoto Oscillators ◽  
Applicable Range ◽  
The Kuramoto Model ◽  
Complete Frequency

The synchronous dynamics of many limit-cycle oscillators can be described by phase models. The Kuramoto model serves as a prototype model for phase synchronization and has been extensively studied in the last 40 years. In this paper, we deal with the complete synchronization problem of the Kuramoto model with frustrations on a complete graph. We study the robustness of complete synchronization with respect to the network structure and the interaction frustrations, and provide sufficient frameworks leading to the complete synchronization, in which all frequency differences of oscillators tend to zero asymptotically. For a uniform frustration and unit capacity, we extend the applicable range of initial configurations for the complete synchronization to be distributed on larger arcs than a half circle by analyzing the detailed dynamics of the order parameters. This improves the earlier results [S.-Y. Ha, H. Kim and J. Park, Remarks on the complete frequency synchronization of Kuramoto oscillators, Nonlinearity 28 (2015) 1441–1462; Z. Li and S.-Y. Ha, Uniqueness and well-ordering of emergent phase-locked states for the Kuramoto model with frustration and inertia, Math. Models Methods Appl. Sci. 26 (2016) 357–382.] which can be applicable only for initial configurations confined in a half circle.

THE BIRTH AND DEATH PROCESSES OF HYPERCYCLE SPIRALS

2003 ◽  
Vol 06 (04) ◽  
pp. 515-535
Author(s):  
KAZUMASA OIDA
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Phase Synchronization ◽  
Occurrence Rate ◽  
Two Dimensional ◽  
Archimedean Spiral ◽  
Simulation Experiments ◽  
Birth And Death Processes ◽  
Long Time ◽  
Random Walk Simulation

The behavior of hypercycle spirals in a two-dimensional cellular automaton model is analyzed. Each spiral can be approximated by an Archimedean spiral with center, width, and phase change according to Brownian motion. A barrier exists between two spirals if the phase synchronization hypothesis is taken into account, and the occurrence rate of pair decay (simultaneous disappearance of two spirals) can be explained through a random walk simulation with the barrier. Simulation experiments show that adjacent species violation is necessary to create new spirals. A hypercycle system can live for a long time if spirals in the system are somewhat unstable, since new spirals cannot emerge when existing spirals are too stable.

scholarly journals Almost global convergence to practical synchronization in the generalized Kuramoto model on networks over the n-sphere

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Johan Markdahl ◽  
Daniele Proverbio ◽  
La Mi ◽  
Jorge Goncalves
Keyword(s):  
Multiple Equilibria ◽  
Phase Synchronization ◽  
Initial Conditions ◽  
Small Diameter ◽  
Kuramoto Model ◽  
Model Parameters ◽  
Robot Swarms ◽  
The Kuramoto Model ◽  
Almost All ◽  
Special Case

AbstractFrom the flashing of fireflies to autonomous robot swarms, synchronization phenomena are ubiquitous in nature and technology. They are commonly described by the Kuramoto model that, in this paper, we generalise to networks over n-dimensional spheres. We show that, for almost all initial conditions, the sphere model converges to a set with small diameter if the model parameters satisfy a given bound. Moreover, for even n, a special case of the generalized model can achieve phase synchronization with nonidentical frequency parameters. These results contrast with the standard n = 1 Kuramoto model, which is multistable (i.e., has multiple equilibria), and converges to phase synchronization only if the frequency parameters are identical. Hence, this paper shows that the generalized network Kuramoto models for n ≥ 2 displays more coherent and predictable behavior than the standard n = 1 model, a desirable property both in flocks of animals and for robot control.

scholarly journals On the Fluid Dynamical Effects of Synchronization in Side-by-Side Swimmers

Biomimetics ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 77 ◽  
Author(s):  
Ramiro Godoy-Diana ◽  
Jérôme Vacher ◽  
Veronica Raspa ◽  
Benjamin Thiria
Keyword(s):  
Particle Image ◽  
Phase Synchronization ◽  
Swimming Performance ◽  
Symmetry Plane ◽  
Water Tank ◽  
Two Dimensional ◽  
Kinematic Parameters ◽  
Image Velocimetry ◽  
Coherent Jet ◽  
Flexible Foils

In-phase and anti-phase synchronization of neighboring swimmers is examined experimentally using two self-propelled independent flexible foils swimming side-by-side in a water tank. The foils are actuated by pitching oscillations at one extremity—the head of the swimmers—and the flow engendered by their undulations is analyzed using two-dimensional particle image velocimetry in their frontal symmetry plane. Following recent observations on the behavior of real fish, we focus on the comparison between in-phase and anti-phase actuation by fixing all other geometric and kinematic parameters. We show that swimming with a neighbor is beneficial for both synchronizations tested, as compared to swimming alone, with an advantage for the anti-phase synchronization. We show that the advantage of anti-phase synchronization in terms of swimming performance for the two-foil “school” results from the emergence of a periodic coherent jet between the two swimmers.

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