Browsing Mathematics by Author "Ashwin, Peter"
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Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators
Ashwin, Peter; Borresen, Jon (American Physical Society, 2004)We study properties of the dynamics underlying slow cluster oscillations in two systems of five globally coupled oscillators. These slow oscillations are due to the appearance of structurally stable heteroclinic connections ... 
Excitability in ramped systems: the compostbomb instability
Wieczorek, Sebastian; Ashwin, Peter; Luke, Catherine M.; Cox, Peter M. (Royal Society, 2011)The paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable ... 
Extreme Sensitivity to Detuning for Globally Coupled Phase Oscillators
Ashwin, Peter; Burylko, Oleksandr; Maistrenko, Yuri; Popovych, Oleksandr (American Physical Society, 2006)We discuss the sensitivity of a population of coupled oscillators to differences in their natural frequencies, i.e., to detuning. We argue that for three or more oscillators, one can get great sensitivity even if the ... 
Fast simulation of phasechange processes in chalcogenide alloys using a Gillespietype cellular automata approach
Ashwin, Peter; Patnaik, B. S. V.; Wright, C. David (American Institute of Physics, 2008)A stochastic cellular automata simulator capable of spatiotemporal modeling of the crystallization and amorphization behavior of phasechange materials during the complex annealing cycles used in optical and electrical ... 
Front propagation in a phase field model with phasedependent heat absorption
Blyuss, Konstantin; Ashwin, Peter; Wright, C. David; Bassom, Andrew P. (Elsevier, 2006)We present a model for the spatiotemporal behaviour of films exposed to radiative heating, where the film can change reversibly between amorphous (glassy) and crystalline states. Such phase change materials are used ... 
Group theoretic conditions for existence of robust relative homoclinic trajectories
Ashwin, Peter; Montaldi, James (Cambridge University Press, 2002)We consider robust relative homoclinic trajectories (RHTs) for Gequivariant vector fields. We give some conditions on the group and representation that imply existence of equivariant vector fields with such trajectories. ... 
Heteroclinic Ratchets in Networks of Coupled Oscillators (published title)
Karabacak, Ozkan; Ashwin, Peter (Springer Verlag, 2010)We analyze an example system of four coupled phase oscillators and discover a novel phenomenon that we call a “heteroclinic ratchet”; a particular type of robust heteroclinic network on a torus where connections wind in ... 
Hopf bifurcation with cubic symmetry and instability of ABC
Ashwin, Peter; Podvigina, Olga (Royal Society, 2003)We examine the dynamics of generic Hopf bifurcation in a system that is symmetric under the action of the rotational symmetries of the cube. We classify the generic branches of periodic solutions at bifurcation; there are ... 
Hypermeander of spirals: local bifurcations and statistical properties
Ashwin, Peter; Melbourne, Ian; Nicol, Matthew (Elsevier, 2001)In both experimental studies and numerical simulations of waves in excitable media, rigidly rotating spiral waves are observed to undergo transitions to complicated spatial dynamics with longterm Brownianlike motion of ... 
Infinities of stable periodic orbits in systems of coupled oscillators
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob (American Physical Society, 2002)We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free ... 
Influence of noise on scalings for inout intermittency
Ashwin, Peter; Covas, Eurico; Tavakol, Reza (American Physical Society, 2001)We study the effects of noise on a recently discovered form of intermittency, referred to as inout intermittency. This type of intermittency, which reduces to onoff in systems with a skew product structure, has been found ... 
Invariant curves and explosion of periodic Islands in systems of piecewise rotations
Ashwin, Peter; Goetz, Arek (Society for Industrial and Applied Mathematics, 2005)Invertible piecewise isometric maps (PWIs) of the plane, in spite of their apparent simplicity, can show a remarkable number of dynamical features analogous to those found in nonlinear smooth area preserving maps. There ... 
Invariant sets for discontinuous parabolic areapreserving torus maps
Ashwin, Peter; Fu, XinChu; Nishikawa, Takashi; Zyczkowski, Karol (Institute of Physics, 2000)We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter ... 
In–out intermittency in partial differential equation and ordinary differential equation models
Covas, Eurico; Tavakol, Reza; Ashwin, Peter; Tworkowski, Andrew; Brooke, John M. (American Institute of Physics, 2001)We find concrete evidence for a recently discovered form of intermittency, referred to as in–out intermittency, in both partial differential equation (PDE) and ordinary differential equation (ODE) models of mean field ... 
Learning of spatio–temporal codes in a coupled oscillator system
Orosz, Gábor; Ashwin, Peter; Townley, Stuart (IEEE, 2009)In this paper, we consider a learning strategy that allows one to transmit information between two coupled phase oscillator systems (called teaching and learning systems) via frequency adaptation. The dynamics of these ... 
A lowdimensional model of binocular rivalry using winnerless competition
Ashwin, Peter; Lavric, Aureliu (Elsevier, 2010)We discuss a novel minimal model for binocular rivalry (and more generally perceptual dominance) effects. The model has only three state variables, but nonetheless exhibits a wide range of input and noisedependent switching. ... 
Masterequation approach to the study of phasechange processes in data storage media
Blyuss, Konstantin; Ashwin, Peter; Bassom, Andrew P.; Wright, C. David (American Physical Society, 2005)We study the dynamics of crystallization in phasechange materials using a masterequation approach in which the state of the crystallizing material is described by a cluster size distribution function. A model is developed ... 
Masterequation approach to understanding multistate phasechange memories and processors
Wright, C. David; Blyuss, Konstantin; Ashwin, Peter (American Institute of Physics, 2007)A masterequation approach is used to perform dynamic modeling of phasetransformation processes that define the operating regimes and performance attributes of electronic (and optical) processors and multistate memory ... 
The middle Pleistocene transition as a generic bifurcation on a slow manifold
Ashwin, Peter; Ditlevsen, Peter (Springer Verlag, 2015)The Quaternary period has been characterised by a cyclical series of glaciations, which are attributed to the change in the insolation (incoming solar radiation) from changes in the Earth’s orbit around the Sun. The spectral ... 
Minimal attractors and bifurcations of random dynamical systems
Ashwin, Peter (Royal Society, 1999)We consider attractors for certain types of random dynamical systems. These are skewproduct systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors ...