Browsing College of Engineering, Mathematics and Physical Sciences by Author "Ashwin, Peter"
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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 ... 
Phase resetting effects for robust cycles between chaotic sets
Ashwin, Peter; Field, Michael; Rucklidge, Alastair M.; Sturman, Rob (American Institute of Physics, 2003)In the presence of symmetries or invariant subspaces, attractors in dynamical systems can become very complicated, owing to the interaction with the invariant subspaces. This gives rise to a number of new phenomena, including ... 
Phasechange technologies: from PCRAM to probestorage to processors
Wright, C. David; Ashawaraya, S.; Ashwin, Peter; Aziz, Mustafa M.; Hicken, R.J.; Kohary, Krisztian; Liu, Y.; Marmier, Arnaud; Shah, P.; Vazquez Diosdado, Jorge A.; Wang, Lei (2010)Phasechange materials based on chalcogenide alloys, for example GeSbTe and AgInSbTe, show remarkable properties such as: the ability to be crystallized by pulses in the (hundreds of) femtoseconds region while at the same ... 
A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy
Benjamin, Oscar; Fitzgerald, Thomas H.B.; Ashwin, Peter; TsanevaAtanasova, Krasimira; Chowdhury, Fahmida; Richardson, Mark P.; Terry, John R. (BioMed Central / SpringerOpen, 2012)We describe a phenomenological model of seizure initiation, consisting of a bistable switch between stable fixed point and stable limitcycle attractors. We determine a quasianalytic formula for the exit time problem for ... 
Polygonal invariant curves for a planar piecewise isometry
Ashwin, Peter; Goetz, Arek (American Mathematical Society, 2005)We investigate a remarkable new planar piecewise isometry whose generating map is a permutation of four cones. For this system we prove the coexistence of an infinite number of periodic components and an uncountable number ... 
Product dynamics for homoclinic attractors
Ashwin, Peter; Field, Michael (Royal Society, 2005)Heteroclinic cycles may occur as structurally stable asymptotically stable attractors if there are invariant subspaces or symmetries of a dynamical system. Even for cycles between equilibria, it may be difficult to obtain ... 
Properties of the invariant disk packing in a model bandpass sigmadelta modulator
Ashwin, Peter; Fu, XinChu; Deane, Jonathan (13 (3), pp. 631641, 2003)In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Σ–Δ modulator. The periodically coded regions form a packing of the forward invariant phase space ... 
Queueing induced by bidirectional motor motion near the end of a microtubule
Ashwin, Peter; Lin, Congping; Steinberg, Gero (201011)Recent live observations of motors in longrange microtubule (MT) dependent transport in the fungus Ustilago maydis have reported bidirectional motion of dynein and an accumulation of the motors at the polymerizationactive ... 
Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators
Ashwin, Peter; Dangelmayr, Gerhard (Taylor & Francis, 2005)Systems of coupled oscillators may exhibit spontaneous dynamical formation of attracting synchronized clusters with broken symmetry; this can be helpful in modelling various physical processes. Analytical computation of ... 
Riddling and invariance for discontinuous maps preserving Lebesgue measure
Ashwin, Peter; Fu, XinChu; Terry, John R. (Institute of Physics, 2002)In this paper we use the mixture of topological and measuretheoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve twodimensional ...