Browsing College of Engineering, Mathematics and Physical Sciences by Author "Ashwin, Peter"
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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 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 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 ... 
Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria
Hawker, David; Ashwin, Peter (World Scientific Publishing Company, 2005)Robust attracting heteroclinic cycles have been found in many models of dynamics with symmetries. In all previous examples, robust heteroclinic cycles appear between a number of symmetry broken equilibria. In this paper ... 
Structure and dynamics of ER: minimal networks and biophysical constraints.
Lin, Congping; Zhang, Yiwei; Sparkes, Imogen; Ashwin, Peter (Biophysical Society, 2014)The endoplasmic reticulum (ER) in live cells is a highly mobile network whose structure dynamically changes on a number of timescales. The role of such drastic changes in any system is unclear, although there are correlations ... 
Symbolic analysis for some planar piecewise linear maps
Fu, XinChu; Ashwin, Peter (American Institute of Mathematical Sciences, 2003)In this paper a class of linear maps on the 2torus and some planar piecewise isometries are discussed. For these discontinuous maps, by introducing codings underlying the map operations, symbolic descriptions of the ... 
Symbolic representation of iterated maps
Fu, XinChu; Lu, Weiping; Ashwin, Peter; Duan, Jinqiao (Schauder University Centre for Nonlinear Studies, 2001)This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map ... 
Synchronization of chaos in an array of three lasers
Terry, John R.; Thornburg, K. Scott; DeShazer, David J.; VanWiggeren, Gregory D.; Zhu, Shiqun; Ashwin, Peter; Roy, Rajarshi (American Physical Society, 1999)Synchronization of the chaotic intensity fluctuations of three modulated Nd:YAG lasers oriented in a linear array with either a modulated pump or loss is investigated experimentally, numerically, and analytically. ... 
Tangencies in invariant disc packings for certain planar piecewise isometries are rare
Ashwin, Peter; Fu, XinChu (Taylor & Francis, 2001)For planar piecewise isometries (PWIs) (twodimensional maps that restrict to isometries on some partition) there is a natural coding given by the itinerary of a trajectory between the pieces (atoms) of the partition on ...