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- Publications
- Influence
The dynamics ofn weakly coupled identical oscillators
- P. Ashwin, J. W. Swift
- Mathematics
- 1 March 1992
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 in… Expand
From attractor to chaotic saddle: a tale of transverse instability
- P. Ashwin, J. Buescu, I. Stewart
- Mathematics
- 1 May 1996
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 the… Expand
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, stretch… Expand
On local attraction properties and a stability index for heteroclinic connections
- O. Podvigina, P. Ashwin
- Mathematics, Physics
- 18 August 2010
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, we… Expand
Travelling fronts for the KPP equation with spatio-temporal delay
- P. Ashwin, M. Bartuccelli, T. Bridges, S. A. Gourley
- Mathematics
- 2002
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 of… Expand
THE SYMMETRY PERSPECTIVE: FROM EQUILIBRIUM TO CHAOS IN PHASE SPACE AND PHYSICAL SPACE (Progress in Mathematics 200)
- P. Ashwin
- Mathematics
- 1 May 2003
Bubbling of attractors and synchronisation of chaotic oscillators
- P. Ashwin, J. Buescu, I. Stewart
- Physics
- 26 September 1994
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 of… Expand
The middle Pleistocene transition as a generic bifurcation on a slow manifold
- P. Ashwin, P. Ditlevsen
- Physics, Geology
- Climate Dynamics
- 14 February 2015
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 orbit… Expand
Three identical oscillators with symmetric coupling
- P. Ashwin, G. P. King, J. W. Swift
- Mathematics
- 1 August 1990
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 S3… Expand
Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators
- P. Ashwin, O. Burylko, Y. Maistrenko
- Mathematics
- 1 April 2008
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 . This… Expand