Now showing items 6-25 of 38

  • Blowout bifurcation in a system of coupled chaotic lasers 

    Ashwin, Peter; Terry, John R.; Thornburg, K. Scott; Roy, Rajarshi (American Physical Society, 1998)
    We show that loss of synchronization of two identical coupled chaotic class B lasers can occur via a blowout bifurcation. This occurs when a transverse Lyapunov exponent governing the stability of a synchronized subspace ...
  • Classification of robust heteroclinic cycles for vector fields in R3 with symmetry 

    Hawker, David; Ashwin, Peter (Institute of Physics, 2005)
    We consider a classification of robust heteroclinic cycles in the positive octant of R3 under the action of the symmetry group (Z2)3. We introduce a coding system to represent different classes up to a topological equivalence, ...
  • Convergence to local random attractors 

    Ashwin, Peter; Ochs, Gunter (Taylor & Francis, 2003)
    Random attractors allow one to classify qualitative and quantitative aspects of the long-time behaviour of stochastically forced systems viewed as random dynamical systems (RDS) in an analogous way to attractors for ...
  • Cycling chaotic attractors in two models for dynamics with invariant subspaces 

    Ashwin, Peter; Rucklidge, Alastair M.; Sturman, Rob (American Institute of Physics, 2004)
    Nonergodic attractors can robustly appear in symmetric systems as structurally stable cycles between saddle-type invariant sets. These saddles may be chaotic giving rise to "cycling chaos." The robustness of such attractors ...
  • Decelerating defects and non-ergodic critical behaviour in a unidirectionally coupled map lattice 

    Ashwin, Peter; Sturman, Rob (Elsevier, 2003)
    We examine a coupled map lattice (CML) consisting of an infinite chain of logistic maps coupled in one direction by inhibitory coupling. We find that for sufficiently strong coupling strength there are dynamical states ...
  • Discrete computation using a perturbed heteroclinic network 

    Ashwin, Peter; Borresen, Jon (Elsevier, 2005)
    Transient synchronization into clusters appears in many biological and physical systems and seems to be important for computation within neural systems. In this paper we show how one can robustly and effectively perform ...
  • Dynamics on networks of cluster states for globally coupled phase oscillators 

    Ashwin, Peter; Orosz, Gábor; Wordsworth, John; Townley, Stuart (Society for Industrial and Applied Mathematics, 2007)
    Systems of globally coupled phase oscillators can have robust attractors that are heteroclinic networks. We investigate such a heteroclinic network between partially synchronized states where the phases cluster into three ...
  • Elliptic behaviour in the sawtooth standard map 

    Ashwin, Peter (Elsevier, 1997)
    This paper examines the standard map with sawtooth nonlinearity when the eigenvalues of the Jacobian lie on the unit circle. This is an area-preserving map of the torus to itself that is linear except on a line on which ...
  • Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators 

    Ashwin, Peter; Borresen, Jon (American Physical Society, 2004)
    We study properties of the dynamics underlying slow cluster oscillations in two systems of five globally coupled oscillators. These slow oscillations are due to the appearance of structurally stable heteroclinic connections ...
  • Extreme Sensitivity to Detuning for Globally Coupled Phase Oscillators 

    Ashwin, Peter; Burylko, Oleksandr; Maistrenko, Yuri; Popovych, Oleksandr (American Physical Society, 2006)
    We discuss the sensitivity of a population of coupled oscillators to differences in their natural frequencies, i.e., to detuning. We argue that for three or more oscillators, one can get great sensitivity even if the ...
  • Fast simulation of phase-change processes in chalcogenide alloys using a Gillespie-type cellular automata approach 

    Ashwin, Peter; Patnaik, B. S. V.; Wright, C. David (American Institute of Physics, 2008)
    A stochastic cellular automata simulator capable of spatiotemporal modeling of the crystallization and amorphization behavior of phase-change materials during the complex annealing cycles used in optical and electrical ...
  • Front propagation in a phase field model with phase-dependent heat absorption 

    Blyuss, Konstantin; Ashwin, Peter; Wright, C. David; Bassom, Andrew P. (Elsevier, 2006)
    We present a model for the spatio-temporal behaviour of films exposed to radiative heating, where the film can change reversibly between amorphous (glassy) and crystalline states. Such phase change materials are used ...
  • 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 ...
  • 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 ...
  • 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 ...