Browsing Centre for Systems, Dynamics and Control by Title
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Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators
(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
(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
(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
(Taylor & Francis, 2003)Random attractors allow one to classify qualitative and quantitative aspects of the longtime 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
(American Institute of Physics, 2004)Nonergodic attractors can robustly appear in symmetric systems as structurally stable cycles between saddletype invariant sets. These saddles may be chaotic giving rise to "cycling chaos." The robustness of such attractors ... 
Decelerating defects and nonergodic critical behaviour in a unidirectionally coupled map lattice
(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
(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
(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
(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
(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
(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
(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
(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
(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. ... 
Hopf bifurcation with cubic symmetry and instability of ABC
(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
(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 ... 
Infinities of stable periodic orbits in systems of coupled oscillators
(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
(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
(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 ... 
Masterequation approach to the study of phasechange processes in data storage media
(American Physical Society, 2005)We study the dynamics of crystallization in phasechange materials using a masterequation approach in which the state of the crystallizing material is described by a cluster size distribution function. A model is developed ...