Browsing College of Engineering, Mathematics and Physical Sciences by Author "Ashwin, Peter"
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Local and global stability indices for a riddled basin attractor of a piecewise linear map
Mohd Roslan, UA; Ashwin, Peter (Taylor & Francis, 20160129)We consider a piecewise expanding linear map with a Milnor attractor whose basin is riddled with the basin of a second attractor. To characterize the local geometry of this riddled basin, we calculate a stability index for ... 
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 ... 
Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience.
Ashwin, Peter; Coombes, S; Nicks, R (BioMed Central, 20160106)The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, ... 
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 ... 
Motormediated bidirectional transport along an antipolar microtubule bundle: A mathematical model
Lin, Congping; Ashwin, Peter; Steinberg, Gero (American Physical Society, 2013)Longdistance bidirectional transport of organelles depends on the coordinated motion of various motor proteins on the cytoskeleton. Recent quantitative live cell imaging in the elongated hyphal cells of Ustilago maydis ... 
Multicluster dynamics in coupled phase oscillator networks
Ismail, Asma; Ashwin, Peter (Taylor & Francis, 2014)In this paper we examine robust clustering behaviour with multiple nontrivial clusters for identically and globally coupled phase oscillators. These systems are such that the dynamics is completely determined by the number ... 
Noiseinduced switching near a depth two heteroclinic network and an application to Boussinesq convection
Ashwin, Peter; Podvigina, Olga (American Institute of Physics (AIP), 2010)We investigate the robust heteroclinic dynamics arising in a system of ordinary differential equations in R4 with symmetry D4⋉(Z2)2. This system arises from the normal form reduction of a 1:2√ mode interaction for Boussinesq ... 
Nonnormal parameter blowout bifurcation: an example in a truncated mean field dynamo model
Covas, Eurico; Ashwin, Peter; Tavakol, Reza (American Physical Society, 1997)We examine global dynamics and bifurcations occurring in a truncated model of a stellar mean field dynamo. This model has symmetryforced invariant subspaces for the dynamics and we find examples of transient type I ... 
On designing heteroclinic networks from graphs
Ashwin, Peter; Postlethwaite, Claire (Elsevier, 2013)Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood ... 
On local attraction properties and a stability index for heteroclinic connections
Podvigina, Olga; Ashwin, Peter (Institute of Physics, 2011) 
On riddling and weak attractors
Ashwin, Peter; Terry, John R. (Elsevier, 2000)We propose general definitions for riddling and partial riddling of a subset V of Rm with nonzero Lebesgue measure and show that these properties are invariant for a large class of dynamical systems. We introduce the ... 
On statistical attractors and the convergence of time averages
Karabacak, Ozkan; Ashwin, Peter (Cambridge University Press / Cambridge Philosophical Society, 2011)There are various notions of attractor in the literature, including measure (Milnor) attractors and statistical (Ilyashenko) attractors. In this paper we relate the notion of statistical attractor to that of the essential ... 
On the geometry of orientationpreserving planar piecewise isometries
Ashwin, Peter; Fu, XinChu (Springer, 2002)Planar piecewise isometries (PWIs) are iterated mappings of subsets of the plane that preserve length (and hence angle and area) on each of a number of disjoint regions. They arise naturally in several applications and are ... 
On the unfolding of a blowout bifurcation
Ashwin, Peter; Aston, Philip J.; Nicol, Matthew (Elsevier, 1998)Suppose a chaotic attractor A in an invariant subspace loses stability on varying a parameter. At the point of loss of stability, the most positive Lyapunov exponent of the natural measure on A crosses zero at what has ... 
Packings induced by piecewise isometries cannot contain the Arbelos
Trovati, Marcello; Ashwin, Peter; Byott, Nigel P. (American Institute of Mathematical Sciences (AIMS), 2008)Planar piecewise isometries with convex polygonal atoms that are piecewise irrational rotations can naturally generate a packing of phase space given by periodic cells that are discs. We show that such packings cannot ... 
Parameter shifts for nonautonomous systems in low dimension: Bifurcation and Rateinduced tipping
Ashwin, Peter; Perryman, C; Wieczorek, Sebastian (arXiv.org, 20150625)We discuss the nonlinear phenomena of irreversible tipping for nonautonomous systems where timevarying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We define notions of bifurcationinduced ... 
Pattern selection: the importance of "how you get there"
Ashwin, Peter; Zaikin, Alexey (Biophysical Society / Elsevier, 20150324)