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Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a complicated structure determined to a large extent by the constraints and dimension of the system. As these networks are of great interest as dynamical models of biological and cognitive… (More)

- Claire M Postlethwaite, Pieta Brown, Todd E Dennis
- Journal of theoretical biology
- 2013

We present a new measure for analysing animal movement data, which we term a 'Multi-Scale Straightness Index' (MSSI). The measure is a generalisation of the 'Straightness Index', the ratio of the beeline distance between the start and end of a track to the total distance travelled. In our new measure, the Straightness Index is computed repeatedly for track… (More)

- Claire M Postlethwaite, Tiffany M Psemeneki, Jangir Selimkhanov, Mary Silber, Malcolm A MacIver
- Journal of the Royal Society, Interface
- 2009

Animal behaviour arises through a complex mixture of biomechanical, neuronal, sensory and control constraints. By focusing on a simple, stereotyped movement, the prey capture strike of a weakly electric fish, we show that the trajectory of a strike is one which minimizes effort. Specifically, we model the fish as a rigid ellipsoid moving through a fluid… (More)

- Claire M. Postlethwaite, Todd E. Dennis
- PloS one
- 2013

Recently, there has been much interest in describing the behaviour of animals by fitting various movement models to tracking data. Despite this interest, little is known about how the temporal 'grain' of movement trajectories affects the outputs of such models, and how behaviours classified at one timescale may differ from those classified at other scales.… (More)

- Peter Ashwin, Claire M. Postlethwaite
- J. Nonlinear Science
- 2016

- C M Postlethwaite, G Brown, M Silber
- Philosophical transactions. Series A…
- 2013

Symmetry-breaking Hopf bifurcation problems arise naturally in studies of pattern formation. These equivariant Hopf bifurcations may generically result in multiple solution branches bifurcating simultaneously from a fully symmetric equilibrium state. The equivariant Hopf bifurcation theorem classifies these solution branches in terms of their symmetries,… (More)

Spatially extended versions of the cyclic-dominance Rock–Paper–Scissors model have traveling wave (in one dimension) and spiral (in two dimensions) behavior. The far field of the spirals behave like traveling waves, which themselves have profiles reminiscent of heteroclinic cycles. We compute numerically a nonlinear dispersion relation between the… (More)

- Claire M Postlethwaite, Michael M Walker
- Journal of theoretical biology
- 2011

All mobile animals respond to gradients in signals in their environment, such as light, sound, odours and magnetic and electric fields, but it remains controversial how they might use these signals to navigate over long distances. The Earth's surface is essentially two-dimensional, so two stimuli are needed to act as coordinates for navigation. However, no… (More)

Robust heteroclinic cycles between equilibria lose stability either through local bifurcations of their equilibria or through global bifurcations. This paper considers a global loss of stability termed a ‘resonant’ bifurcation. This bifurcation is usually associated with the birth or death of a nearby periodic orbit, and generically occurs in either a… (More)

Previous work has shown that Benjamin–Feir unstable traveling waves of the complex Ginzburg–Landau equation (CGLE) in two spatial dimensions cannot be stabilized using a particular time-delayed feedback control mechanism known as ‘time-delay autosynchronization’. In this paper, we show that the addition of similar spatial feedback terms can be used to… (More)