Browsing Centre for Systems, Dynamics and Control by Title
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The 1 : √2 mode interaction and heteroclinic networks in Boussinesq convection
(Elsevier, 2007)Methods of equivariant bifurcation theory are applied to Boussinesq convection in a plane layer with stressfree horizontal boundaries and an imposed square lattice periodicity in the horizontal directions. We consider ... 
Acceleration of onedimensional mixing by discontinuous mappings
(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 ... 
Adaptive sliding mode observation in a network of dynamical systems
(Wiley Interscience, 20151226)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 ... 
Anisotropic properties of riddled basins
(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
(Elsevier, 1999)This paper examines an electronic oscillator forced by a pseudorandom noise signal. We give evidence of the existence of one or more random attractors for the system depending on noise amplitude and system parameters. ... 
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 ...