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The dynamics ofn weakly coupled identical oscillators
SummaryWe present a framework for analysing arbitrary networks of identical dissipative oscillators assuming weak coupling. Using the symmetry of the network, we find dynamically invariant regions inExpand
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From attractor to chaotic saddle: a tale of transverse instability
Suppose that a dynamical system possesses an invariant submanifold, and the restriction of the system to this submanifold has a chaotic attractor A. Under which conditions is A an attractor for theExpand
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Acceleration of one-dimensional mixing by discontinuous mappings
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, stretchExpand
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On local attraction properties and a stability index for heteroclinic connections
Some invariant sets may attract a nearby set of initial conditions but nonetheless repel a complementary nearby set of initial conditions. For a given invariant set with a basin of attraction N, weExpand
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Travelling fronts for the KPP equation with spatio-temporal delay
Abstract. We study an integro-differential equation based on the KPP equation with a convolution term which introduces a time-delay in the nonlinearity. Special attention is paid to the question ofExpand
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Bubbling of attractors and synchronisation of chaotic oscillators
We present a system of two coupled identical chaotic electronic circuits that exhibit a blowout bifurcation resulting in loss of stability of the synchronised state. We introduce the concept ofExpand
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The middle Pleistocene transition as a generic bifurcation on a slow manifold
The Quaternary period has been characterised by a cyclical series of glaciations, which are attributed to the change in the insolation (incoming solar radiation) from changes in the Earth’s orbitExpand
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Three identical oscillators with symmetric coupling
This paper is theoretical and experimental investigation of three identical oscillators with weak symmetric coupling. The authors find that the dynamics is governed by an ODE on the 2-torus with S3Expand
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Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators
Abstract 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 . ThisExpand
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