Now showing items 31-50 of 68

  • 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 G-equivariant vector fields. We give some conditions on the group and representation that imply existence of equivariant vector fields with such trajectories. ...
  • 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 long-term Brownian-like motion of ...
  • Impact of climate-carbon cycle feedbacks on emissions scenarios to achieve stabilisation 

    Jones, Chris D.; Cox, Peter M.; Huntingford, Chris (Cambridge University Press, 2006-02)
    As atmospheric concentrations of CO2 increase due to burning of fossil fuels, stabilisation scenarios are receiving increasing amounts of interest both politically and scientifically, leading to the question, ‘what emissions ...
  • 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 ...
  • The influence of periodic islands in the flow on a scalar tracer in the presence of a steady source 

    Turner, M. R.; Thuburn, John; Gilbert, Andrew D. (American Institute of Physics, 2009)
    In this paper we examine the influence of periodic islands within a time periodic chaotic flow on the evolution of a scalar tracer. The passive scalar tracer is injected into the flow field by means of a steady source term. ...
  • 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 ...
  • Kinematic dynamo action in large magnetic Reynolds number flows driven by shear and convection 

    Ponty, Y.; Gilbert, Andrew D.; Soward, Andrew M. (Cambridge University Press, 2001)
    A numerical investigation is presented of kinematic dynamo action in a dynamically driven fluid flow. The model isolates basic dynamo processes relevant to field generation in the Solar tachocline. The horizontal plane ...
  • 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 ...
  • Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles 

    Turner, M. R.; Gilbert, Andrew D. (Cambridge University Press, 2007)
    This paper considers the evolution of smooth, two-dimensional vortices subject to a rotating external strain field, which generates regions of recirculating, cat's eye stream line topology within a vortex. When the external ...
  • Master-equation approach to the study of phase-change 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 phase-change materials using a master-equation approach in which the state of the crystallizing material is described by a cluster size distribution function. A model is developed ...
  • Master-equation approach to understanding multistate phase-change memories and processors 

    Wright, C. David; Blyuss, Konstantin; Ashwin, Peter (American Institute of Physics, 2007)
    A master-equation approach is used to perform dynamic modeling of phase-transformation 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 skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors ...
  • Neutral modes of a two-dimensional vortex and their link to persistent cat's eyes 

    Turner, M. R.; Gilbert, Andrew D.; Bassom, Andrew P. (American Institute of Physics, 2008)
    This paper considers the relaxation of a smooth two-dimensional vortex to axisymmetry after the application of an instantaneous, weak external strain field. In this limit the disturbance decays exponentially in time at a ...
  • Nonlinear dynamo action in rotating convection and shear 

    Zhang, Pu; Gilbert, Andrew D.; Zhang, Keke (Cambridge University Press, 2005)
    Magnetic field amplification by the motion of an electrically conducting fluid is studied, using a rotating plane-layer geometry. The fluid flow is driven by convection, and by a moving bottom boundary, which leads to an ...
  • Nonlinear equilibration of a dynamo in a smooth helical flow 

    Bassom, Andrew P.; Gilbert, Andrew D. (Cambridge University Press, 1997)
    We investigate the nonlinear equilibration of magnetic fields in a smooth helical flow at large Reynolds number Re and magnetic Reynolds number Rm with Re >> Rm >> 1. We start with a smooth spiral Couette flow driven by ...
  • Nonlinear solutions of the amplitude equations governing fluid flow in rotating spherical geometries 

    Blockley, Edward William (University of ExeterMathematical Sciences, 2008-09-08)
    We are interested in the onset of instability of the axisymmetric flow between two concentric spherical shells that differentially rotate about a common axis in the narrow-gap limit. The expected mode of instability takes ...
  • 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 non-zero Lebesgue measure and show that these properties are invariant for a large class of dynamical systems. We introduce the ...
  • On the geometry of orientation-preserving planar piecewise isometries 

    Ashwin, Peter; Fu, Xin-Chu (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 ...