Browsing Mathematics Research Institute (MRI) 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 ... 
Accelerated diffusion in the centre of a vortex
(Cambridge University Press, 2001)The spiral windup and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P1/3 times the turnover ... 
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. ... 
Biclustering models for structured microarray data
(IEEE, 2005)Microarrays have become a standard tool for investigating gene function and more complex microarray experiments are increasingly being conducted. For example, an experiment may involve samples from several groups or may ... 
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 ... 
The carbon cycle response to ENSO: a coupled climate–carbon cycle model study
(American Meteorological Society, 2001)There is significant interannual variability in the atmospheric concentration of carbon dioxide (CO2) even when the effect of anthropogenic sources has been accounted for. This variability is well correlated with the El ... 
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, ... 
Climate–carbon cycle feedback analysis: results from the C4MIP model intercomparison
(American Meteorological Society, 2006)Eleven coupled climatecarbon cycle models used a common protocol to study the coupling between climate change and the carbon cycle. The models were forced by historical emissions and the Intergovernmental Panel on Climate ... 
Comparing the degree of land–atmosphere interaction in four atmospheric general circulation models
(American Meteorological Society, 2002)The strength of the coupling between the land and the atmosphere, which controls, for example, the degree to which precipitationinduced soil moisture anomalies affect the overlying atmosphere and thereby the subsequent ... 
Conditions for sinktosource transitions and runaway feedbacks from the land carbon cycle
(Cambridge University Press, 200602)The first GCM climatecarbon cycle simulation indicated that the land biosphere could provide a significant acceleration of 21st century climate change (Cox et al. 2000). In this numerical experiment the carbon storage was ... 
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 ... 
Effective diffusion of scalar fields in a chaotic flow
(American Institute of Physics, 2008)The advection of a tracer field in a fluid flow can create complex scalar structures and increase the effect of weak diffusion by orders of magnitude. One tool to quantify this is to measure the flux of scalar across contour ...