Browsing Mathematics Research Institute (MRI) by Author "Ashwin, Peter"
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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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
Twostate intermittency near a symmetric interaction of saddlenode and Hopf bifurcations: a case study from dynamo theory
Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob (Elsevier, 2004)We consider a model of a Hopf bifurcation interacting as a codimension 2 bifurcation with a saddlenode on a limit cycle, motivated by a loworder model for magnetic activity in a stellar dynamo. This model consists of ...