Zobrazeno 1 - 10
of 310
pro vyhledávání: '"Lloyd, David J."'
Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular Restricted Three-
Externí odkaz:
http://arxiv.org/abs/2405.18909
Data-driven modelling techniques provide a method for deriving models of dynamical systems directly from complicated data streams. However, tracking and forecasting such data streams poses a significant challenge to most methods, as they assume the u
Externí odkaz:
http://arxiv.org/abs/2405.02166
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and hexagons)
Externí odkaz:
http://arxiv.org/abs/2404.14987
Autor:
Hill, Dan J., Lloyd, David J. B.
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this emergence or c
Externí odkaz:
http://arxiv.org/abs/2403.02949
Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its components si
Externí odkaz:
http://arxiv.org/abs/2301.08075
Data assimilation techniques, such as ensemble Kalman filtering, have been shown to be a highly effective and efficient way to combine noisy data with a mathematical model to track and forecast dynamical systems. However, when dealing with high-dimen
Externí odkaz:
http://arxiv.org/abs/2301.05504
Publikováno v:
Nonlinearity 37, 035015 (2024)
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when the patterns
Externí odkaz:
http://arxiv.org/abs/2210.13122
Publikováno v:
Nonlinearity 36, 2567 (2023)
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathematical theory for the emergence of these localised cellular patterns from
Externí odkaz:
http://arxiv.org/abs/2203.09363
Publikováno v:
J. Nonlinear Sci. 31, 79 (2021)
This paper investigates the existence of localised axisymmetric (radial) patterns on the surface of a ferrofluid in the presence of a uniform vertical magnetic field. We formally investigate all possible small-amplitude solutions which remain bounded
Externí odkaz:
http://arxiv.org/abs/2003.12324
Publikováno v:
Phys. Rev. E 102, 032210 (2020)
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on the level
Externí odkaz:
http://arxiv.org/abs/2002.01705