#### Filter Results:

- Full text PDF available (53)

#### Publication Year

1996

2017

- This year (2)
- Last 5 years (18)
- Last 10 years (33)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

#### Method

Learn More

- Hinke M. Osinga, Jan Wiersig, Paul Glendinning, Ulrike Feudel
- I. J. Bifurcation and Chaos
- 2001

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked behavior with a unique attracting periodic orbit. Under the influence of quasiperiodic forcing the dynamics of the map… (More)

- J. Stark, Paul Glendinning
- 2000

Rotation numbers have played a central role in the study of (unforced) monotone circle maps. In such a case it is possible to obtain a priori bounds of the form »¡ 1=n μ ...1=n†...yn ¡ y0† μ »‡ 1=n, where ...1=n†...yn ¡ y0† is an estimate of the rotation number obtained from an orbit of length n with initial condition y0, and » is the true rotation number.… (More)

- Piotr Kowalczyk, Paul Glendinning, Martin Brown, Gustavo A. Medrano-Cerda, Houman Dallali, Jonathan H. Shapiro
- Journal of the Royal Society, Interface
- 2012

We are interested in understanding the mechanisms behind and the character of the sway motion of healthy human subjects during quiet standing. We assume that a human body can be modelled as a single-link inverted pendulum, and the balance is achieved using linear feedback control. Using these assumptions, we derive a switched model which we then… (More)

- Paul Glendinning
- Proceedings. Biological sciences
- 2004

Motion camouflage is a strategy whereby an aggressor moves towards a target while appearing stationary to the target except for the inevitable change in perceived size of the aggressor as it approaches. The strategy has been observed in insects, and mathematical models using discrete time or neural-network control have been used to simulate the behaviour.… (More)

- Renato Vitolo, Paul Glendinning, Jason A. C. Gallas
- Physical review. E, Statistical, nonlinear, and…
- 2011

Infinite cascades of periodicity hubs were predicted and very recently observed experimentally to organize stable oscillations of some dissipative flows. Here we describe the global mechanism underlying the genesis and organization of networks of periodicity hubs in control parameter space of a simple prototypical flow, namely a Rössler's oscillator. We… (More)

- Paul Glendinning
- 2003

Tennyson’s ‘Nature, red in tooth and claw’ [10] paints a rather more vivid picture of the struggle for life than I encounter on the moors. Moorland deaths seem bloodless; the work of the weather, land and time rather than the result of battles between rival animals. The only regular wars I witness are the squabbles of finches and tits over the peanut… (More)

- Paul Glendinning, Chi Hong Wong
- Physical review. E, Statistical, nonlinear, and…
- 2009

The normal form for codimension 1 border collision bifurcations of fixed points of discrete time piecewise smooth dynamical systems is considered in the unstable case. We show that in appropriate parameter regions there is a snap-back repeller immediately after the bifurcation, and hence that the bifurcation creates chaos. Although the chaotic solutions are… (More)

- Marc Goodfellow, Paul Glendinning
- Journal of mathematical neuroscience
- 2013

We investigate the dynamic mechanisms underlying intermittent state transitions in a recently proposed neural mass model of epilepsy. A low dimensional model is constructed, which preserves two key features of the neural mass model, namely (i) coupling between oscillators and (ii) heterogeneous proximity of these oscillators to a bifurcation between… (More)

Homoclinic orbits to bifocus-type stationary points have been studied theoretically by a number of authors, but up until now, only one analytic example has been found. In this paper we summarise and extend the known theory regarding bifocal homoclinic bifurcations and present numerical verification of some of the more interesting theoretical predictions… (More)

- Piotr Kowalczyk, Paul Glendinning
- Chaos
- 2011

In this paper we study the qualitative dynamics of piecewise-smooth slow-fast systems (singularly perturbed systems) which are everywhere continuous. We consider phase space topology of systems with one-dimensional slow dynamics and one-dimensional fast dynamics. The slow manifold of the reduced system is formed by a piecewise-continuous curve, and the… (More)