Browsing Mathematics by Author "Ashwin, Peter"
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Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation
Aguiar, M.; Ashwin, Peter; Dias, A.; Field, Michael (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 areapreserving 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 ... 
Excitability in ramped systems: the compostbomb instability
Wieczorek, Sebastian; Ashwin, Peter; Luke, Catherine M.; Cox, Peter M. (Royal Society, 2011)The paper studies a novel excitability type where a large excitable response appears when a system’s parameter is varied gradually, or ramped, above some critical rate. This occurs even though there is a (unique) stable ... 
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 phasechange processes in chalcogenide alloys using a Gillespietype 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 phasechange materials during the complex annealing cycles used in optical and electrical ... 
Front propagation in a phase field model with phasedependent heat absorption
Blyuss, Konstantin; Ashwin, Peter; Wright, C. David; Bassom, Andrew P. (Elsevier, 2006)We present a model for the spatiotemporal 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 Gequivariant vector fields. We give some conditions on the group and representation that imply existence of equivariant vector fields with such trajectories. ... 
Heteroclinic Ratchets in Networks of Coupled Oscillators (published title)
Karabacak, Ozkan; Ashwin, Peter (Springer Verlag, 2010)We analyze an example system of four coupled phase oscillators and discover a novel phenomenon that we call a “heteroclinic ratchet”; a particular type of robust heteroclinic network on a torus where connections wind in ... 
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 ... 
Hopf normal form with $S_N$ symmetry and reduction to systems of nonlinearly coupled phase oscillators
Ashwin, Peter; Rodrigues, Ana (Arxiv.org, 201602)Coupled oscillator models where $N$ oscillators are identical and symmetrically coupled to all others with full permutation symmetry $S_N$ are found in a wide variety of applications. Much, but not all, work on phase ... 
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 longterm Brownianlike motion of ... 
Identical phase oscillator networks: bifurcations, symmetry and reversibility for generalized coupling
Ashwin, Peter; Bick, Christian; Burylko, Oleksandr (Cornell University Library, 20160325)For a system of coupled identical phase oscillators with full permutation symmetry, any broken symmetries in dynamical behaviour must come from spontaneous symmetry breaking, i.e. from the nonlinear dynamics of the system. ... 
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 ... 
Influence of noise on scalings for inout intermittency
Ashwin, Peter; Covas, Eurico; Tavakol, Reza (American Physical Society, 2001)We study the effects of noise on a recently discovered form of intermittency, referred to as inout intermittency. This type of intermittency, which reduces to onoff in systems with a skew product structure, has been found ... 
Invariant curves and explosion of periodic Islands in systems of piecewise rotations
Ashwin, Peter; Goetz, Arek (Society for Industrial and Applied Mathematics, 2005)Invertible piecewise isometric maps (PWIs) of the plane, in spite of their apparent simplicity, can show a remarkable number of dynamical features analogous to those found in nonlinear smooth area preserving maps. There ... 
Invariant sets for discontinuous parabolic areapreserving torus maps
Ashwin, Peter; Fu, XinChu; Nishikawa, Takashi; Zyczkowski, Karol (Institute of Physics, 2000)We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter ... 
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 ...