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  • Adaptive sliding mode observation in a network of dynamical systems 

    Prathyush, P. Menon; Edwards, Christopher; Shtessel, Yuri (Wiley Interscience, 2015-12-26)
    This paper considers the problem of reconstructing state information in all the nodes of a complex network of dynamical systems. The individual nodes comprise a known linear part and unknown but bounded uncertainties in ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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, ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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. ...
  • 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 ...
  • 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 ...
  • 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. ...
  • 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 ...
  • 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 ...

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