Browsing Mathematics Research Institute (MRI) 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 ... 
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 ... 
Effects of frozen soil on soil temperature, spring infiltration, and runoff: results from the PILPS 2(d) experiment at Valdai, Russia
(American Meteorological Society, 20091218)The Project for Intercomparison of LandSurface Parameterization Schemes phase 2(d) experiment at Valdai, Russia, offers a unique opportunity to evaluate land surface schemes, especially snow and frozen soil parameterizations. ... 
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 ... 
Energycrossing number relations for braided magnetic fields
(American Physical Society, 1993)This Letter derives lower bounds on the energy of braided magnetic fields, based on crossing number techniques pioneered by Freedman and He. Mean crossing numbers are defined for magnetic fields inside a cylinder; for ... 
Explicit representation of subgrid heterogeneity in a GCM land surface scheme
(American Meteorological Society, 2003)A land surface scheme that may be run with or without a tiled representation of subgrid heterogeneity and includes an implicit atmospheric coupling scheme is described. Simulated average surface air temperatures and diurnal ... 
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 ...