Now showing items 1-20 of 73

  • The 1 : √2 mode interaction and heteroclinic networks in Boussinesq convection 

    Podvigina, Olga; Ashwin, Peter (Elsevier, 2007)
    Methods of equivariant bifurcation theory are applied to Boussinesq convection in a plane layer with stress-free horizontal boundaries and an imposed square lattice periodicity in the horizontal directions. We consider ...
  • Acceleration of one-dimensional mixing by discontinuous mappings 

    Ashwin, Peter; Nicol, Matthew; Kirkby, Norman (Elsevier, 2002)
    The paper considers a simple class of models for mixing of a passive tracer into a bulk material that is essentially one dimensional. We examine the relative rates of mixing due to diffusion, stretch and fold operations ...
  • Anisotropic properties of riddled basins 

    Ashwin, Peter; Breakspear, Michael (Elsevier, 2001)
    We consider some general properties of chaotic attractors with riddled basins of attraction (basins with positive measure but open dense complements) in dynamical systems with symmetries. We investigate how a basin of ...
  • Attractors of a randomly forced electronic oscillator 

    Ashwin, Peter (Elsevier, 1999)
    This paper examines an electronic oscillator forced by a pseudo-random noise signal. We give evidence of the existence of one or more random attractors for the system depending on noise amplitude and system parameters. ...
  • Bidirectional transport and pulsing states in a multi-lane ASEP model 

    Lin, Congping; Steinberg, Gero; Ashwin, Peter (IOP Publishing, 2011)
    In this paper, we introduce an ASEP-like transport model for bidirectional motion of particles on a multi-lane lattice. The model is motivated by {\em in vivo} experiments on organelle motility along a microtubule (MT), ...
  • Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators 

    Ashwin, Peter; Burylko, Oleksandr; Maistrenko, Yuri (Elsevier, 2008)
    We study the bifurcation and dynamical behaviour of the system of N globally coupled identical phase oscillators introduced by Hansel, Mato and Meunier, in the cases N=3 and N=4. This model has been found to exhibit robust ...
  • 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 ...
  • Chaos in symmetric phase oscillator networks 

    Bick, Christian; Timme, Marc; Paulikat, Danilo; Rathlev, Dirk; Ashwin, Peter (American Physical Society, 2011)
    Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization so far has been found to be chaotic ...
  • 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, ...
  • Cone exchange transformations and boundedness of orbits 

    Ashwin, Peter; Goetz, Arek (Cambridge University Press, 2010)
    We introduce a class of two-dimensional piecewise isometries on the plane that we refer to as cone exchange transformations (CETs). These are generalizations of interval exchange transformations (IETs) to 2D unbounded ...
  • 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 ...
  • Criteria for robustness of heteroclinic cycles in neural microcircuits. 

    Ashwin, Peter; Karabacak, Ozkan; Nowotny, Thomas (BioMed Central / SpringerOpen, 2011)
    We introduce a test for robustness of heteroclinic cycles that appear in neural microcircuits modeled as coupled dynamical cells. Robust heteroclinic cycles (RHCs) can appear as robust attractors in Lotka-Volterra-type ...
  • Cycling chaos: its creation, persistence and loss of stability in a model of nonlinear magnetoconvection 

    Ashwin, Peter; Rucklidge, Alastair M. (Elsevier, 1998)
    We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this `cycling chaos' manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant ...
  • 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 ...
  • Designing the dynamics of globally coupled oscillators 

    Orosz, Gábor; Moehlis, Jeff; Ashwin, Peter (Oxford University Press, 2009)
    A method for designing cluster states with prescribed stability is presented for coupled phase oscillator systems with all-to-all coupling. We determine criteria for the coupling function that ensure the existence and ...
  • 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 of coupled cell networks: synchrony, heteroclinic cycles and inflation 

    Aguiar, M.; Ashwin, Peter; Dias, A.; Field, M. (Springer Verlag, 2011)
    We consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two ...
  • 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 ...