Paul Glendinning

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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)
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)
The deterministic border collision normal form describes the bifurcations of a discrete time dynamical system as a fixed point moves across the switching surface with changing parameter. If the position of the switching surface varies randomly, but within some bounded region, we give conditions which imply that the attractor close to the bifurcation point(More)
It is well-known that the dynamics of the Arnol ′ d circle map is phase-locked in regions of the parameter space called Arnol ′ d 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)
The behaviour of light rays obeying Snell's Law in a medium made up of two materials with different refractive indices and which are arranged in a periodic chessboard pattern is described. The analysis is in some ways analogous to the study of rational billiards and uses a return map on one surface to prove, amongst other things, that the number of angles(More)
If a family of piecewise smooth systems depending on a real parameter is defined on two different regions of the plane separated by a switching surface, then a boundary equilibrium bifurcation occurs if a stationary point of one of the systems intersects the switching surface at a critical value of the parameter. We derive the leading order terms of a(More)
The border collision normal form is a continuous piecewise affine map of R n with applications in piecewise smooth bifurcation theory. We show that these maps have absolutely continuous invariant measures for an open set of parameter space and hence that the attractors have Haus-dorff (fractal) dimension n. If n = 2 the attractors have topological dimension(More)
Prior studies indicate that the human translational vestibulo-ocular reflex (tVOR) generates eye rotations approximately half the magnitude required to keep the line of sight pointed at a stationary object--a compensation ratio (CR) of ∼0.5. We asked whether changes of visual or vestibular stimuli could increase the CR of tVOR. First, subjects viewed their(More)
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