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Now showing items 48-67 of 68

  • 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 ...
  • The onset of thermal convection in Ekman–Couette shear flow with oblique rotation 

    Ponty, Y.; Gilbert, Andrew D.; Soward, Andrew M. (Cambridge University Press, 2003)
    The onset of convection of a Boussinesq fluid in a horizontal plane layer is studied. The system rotates with constant angular velocity Ω, which is inclined at an angle ϑ to the vertical. The layer is sheared by keeping ...
  • 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 ...
  • Photospheric flux density of magnetic helicity 

    Pariat, E.; Démoulin, P.; Berger, M.A. (EDP Sciences, 2005)
    Several recent studies have developed the measurement of magnetic helicity flux from the time evolution of photospheric magnetograms. The total flux is computed by summing the flux density over the analyzed region. All ...
  • 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 sigma-delta modulator 

    Ashwin, Peter; Fu, Xin-Chu; Deane, Jonathan (13 (3), pp. 631-641, 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 ...
  • The representation of snow in land surface schemes: results from PILPS 2(d) 

    Slater, Andrew G.; Schlosser, C. Adam; Desborough, C. E.; Pitman, Andrew; Henderson-Sellers, Ann; Robock, Alan; Vinnikov, Konstantin Y.; Mitchell, Ken; Boone, Aaron; Braden, Harald; Chen, F.; Cox, Peter M.; De Rosnay, Patricia; Dickinson, Robert E.; Dai, Yongjiu; Duan, Qingyun; Entin, J.; Etchevers, Pierre; Gedney, Nicola; Gusev, Yevgeniy M.; Habets, Florence; Kim, Jinwon; Koren, V.; Kowalczyk, Eva; Nasonova, Olga N.; Noilhan, Joel; Schaake, John; Shmakin, Andrey B.; Smirnova, Tatiana G.; Verseghy, Diana; Wetzel, Peter; Xue, Yongkang; Yang, Zong-Liang; Zeng, Qing-Cun (American Meteorological Society, 2001)
    Twenty-one land surface schemes (LSSs) performed simulations forced by 18 yr of observed meteorological data from a grassland catchment at Valdai, Russia, as part of the Project for the Intercomparison of Land-Surface ...
  • 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 ...
  • The sensitivity of global climate model simulations to the representation of soil moisture heterogeneity 

    Gedney, Nicola; Cox, Peter M. (American Meteorological Society, 2003)
    Improving the treatment of subgrid-scale soil moisture variations is recognized as a priority for the next generation of land surface schemes. Here, the impact of an improved representation of subgrid-scale soil moisture ...
  • The spiral wind-up and dissipation of vorticity and a passive scalar in a strained planar vortex 

    Bassom, Andrew P.; Gilbert, Andrew D. (Cambridge University Press, 1999)
    The response of a Gaussian vortex to a weak time-dependent external strain field is studied numerically. The cases of an impulsive strain, an on–off step function, and a continuous random strain are considered. Transfers ...
  • The spiral wind-up of vorticity in an inviscid planar vortex 

    Bassom, Andrew P.; Gilbert, Andrew D. (Cambridge University Press, 1998)
    The relaxation of a smooth two-dimensional vortex to axisymmetry, also known as `axisymmetrization', is studied asymptotically and numerically. The vortex is perturbed at t = 0 and differential rotation leads to the wind-up ...
  • 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, Xin-Chu (Taylor & Francis, 2001)
    For planar piecewise isometries (PWIs) (two-dimensional 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 ...
  • Thresholds for the formation of satellites in two-dimensional vortices 

    Turner, M. R.; Gilbert, Andrew D. (Cambridge University Press, 2008)
    This paper examines the evolution of a two-dimensional vortex which initially consists of an axisymmetric monopole vortex with a perturbation of azimuthal wavenumber m = 2 added to it. If the perturbation is weak, then the ...
  • Two-state intermittency near a symmetric interaction of saddle-node 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 saddle-node on a limit cycle, motivated by a low-order model for magnetic activity in a stellar dynamo. This model consists of ...
  • Vortex motion in a weak background shear flow 

    Bajer, Konrad; Bassom, Andrew P.; Gilbert, Andrew D. (Cambridge University Press, 2004)
    A point vortex is introduced into a weak background vorticity gradient at finite Reynolds number. As the vortex spreads viscously so the background vorticity becomes wrapped around it, leading to enhanced diffusion of ...