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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

188 22

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

288 18- PDF

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

32 6

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

39 6- PDF

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

118 5

THE SYMMETRY PERSPECTIVE: FROM EQUILIBRIUM TO CHAOS IN PHASE SPACE AND PHYSICAL SPACE (Progress in Mathematics 200)

- P. Ashwin
- Mathematics
- 1 May 2003

28 5

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

343 4- PDF

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

29 4- PDF

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

70 3

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

52 3- PDF