#### Filter Results:

- Full text PDF available (13)

#### Publication Year

2006

2016

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

#### Organism

Learn 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)

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)

Husdpeth, Magnasco, and collaborators have suggested that the auditory system works by tuning a collection of hair cells near Hopf bifurcation, but each with a different frequency. An incoming sound signal to the cochlea then resonates most strongly with one of these hair cells, which then informs the auditory neuronal system of the frequency of the… (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 bifurca-tion is usually associated with the birth or death of a nearby periodic orbit, and generically occurs in either a… (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)

We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling due to complex eigenvalues in the flow linearised about one of the equilibria common to all cycles in the network. We… (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)

- Claire M Postlethwaite, Mary Silber
- Physical review. E, Statistical, nonlinear, and…
- 2007

For many years it was believed that an unstable periodic orbit with an odd number of real Floquet multipliers greater than unity cannot be stabilized by the time-delayed feedback control mechanism of Pyragas. A recent paper by Fiedler et al. Phys. Rev. Lett. 98, 114101 (2007) uses the normal form of a subcritical Hopf bifurcation to give a counterexample to… (More)

- 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)

- 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)