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Collective coordinate framework to study solitary waves in stochastically perturbed Korteweg-de Vries equations.
Phys Rev E
August 2021
School of Mathematics and Statistics, The University of Sydney, Sydney, New South Wales 2006, Australia.
Stochastically perturbed Korteweg-de Vries (KdV) equations are widely used to describe the effect of random perturbations on coherent solitary waves. We present a collective coordinate approach to describe the effect on coherent solitary waves in stochastically perturbed KdV equations. The collective coordinate approach allows one to reduce the infinite-dimensional stochastic partial differential equation (SPDE) to a finite-dimensional stochastic differential equation for the amplitude, width and location of the solitary wave.
View Article and Find Full Text PDFMesoscopic model reduction for the collective dynamics of sparse coupled oscillator networks.
Chaos
July 2021
School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia.
The behavior at bifurcation from global synchronization to partial synchronization in finite networks of coupled oscillators is a complex phenomenon, involving the intricate dynamics of one or more oscillators with the remaining synchronized oscillators. This is not captured well by standard macroscopic model reduction techniques that capture only the collective behavior of synchronized oscillators in the thermodynamic limit. We introduce two mesoscopic model reductions for finite sparse networks of coupled oscillators to quantitatively capture the dynamics close to bifurcation from global to partial synchronization.
View Article and Find Full Text PDFModel reduction for the Kuramoto-Sakaguchi model: The importance of nonentrained rogue oscillators.
Phys Rev E
June 2020
School of Mathematics and Statistics, The University of Sydney, Sydney, New South Wales, 2006 Australia.
The Kuramoto-Sakaguchi model for coupled phase oscillators with phase frustration is often studied in the thermodynamic limit of infinitely many oscillators. Here we extend a model reduction method based on collective coordinates to capture the collective dynamics of finite-size Kuramoto-Sakaguchi models. We find that the inclusion of the effects of rogue oscillators is essential to obtain an accurate description, in contrast to the original Kuramoto model, where we show that their effects can be ignored.
View Article and Find Full Text PDFChaos in networks of coupled oscillators with multimodal natural frequency distributions.
Chaos
September 2019
School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia.
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with M peaks it is typical that there is a range of coupling strengths such that oscillators belonging to each peak form a synchronized cluster, but the clusters do not globally synchronize. We use collective coordinates to describe the intercluster and intracluster dynamics, which reduces the Kuramoto model to 2M-1 degrees of freedom.
View Article and Find Full Text PDFSolitonlike attractor for blood vessel tip density in angiogenesis.
Phys Rev E
December 2016
G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain.
Recently, numerical simulations of a stochastic model have shown that the density of vessel tips in tumor-induced angiogenesis adopts a solitonlike profile [Sci. Rep. 6, 31296 (2016)2045-232210.
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