UK Nonlinear News, August 2002

Recent thesis

Dynamics of Synaptically Interacting Integrate-and-Fire Neurons

Matthew James

Department of Mathematical Sciences, Loughborough University

Supervisors: Professor Paul Bressloff and Dr S. Coombes


Travelling waves of activity have been experimentally observed in many neural systems. The functional significance of such travelling waves is not always clear. Elucidating the mechanisms of wave initiation, propagation and bifurcation may therefore have a role to play in ascertaining the function of such waves. Previous treatments of travelling waves of neural activity have focused on the mathematical analysis of travelling pulses and numerical studies of travelling waves. It is the aim of this thesis to provide insight into the propagation and = bifurcation of travelling waveforms in biologically realistic systems.

The full abstract and thesis are available online at:

Source: Steve Coombes.

Nonlinear Dynamics of Vibro-Impact Ground Penetration Systems

Ko-Choong Woo

Centre for Applied Dynamics Research, University of Aberdeen

Supervisors: Professor Marian Wiercigroch, Professor Albert A Rodger and Dr Richard D Neilson


This thesis is devoted to the mathematical modelling and analysis of a novel ground moving machine, which utilises a combination of vibrations and impacts to reduce the soil resistance.

Extensive analytical and numerical studies have been carried out on impact oscillators using various nonlinear dynamic techniques including constructing Poincare maps and bifurcation diagrams. Also a systematic methodology to apply the alternating frequency-time harmonic balance method to impact oscillators has been developed .

For effective operation of such a machine, a closed loop feedback system is needed. In view of the feedback in the control system, the issue of the phase shift between the external forcing and the system response was addressed and a practical scheme for calculating and adjusting the phase difference for a piecewise oscillator mimicking a vibro-impact moling machine was devised.

Experimental work was conducted on a prototype machine to verify the theoretical predictions by looking at the displacement of the system and impact forces generated. Spectral analysis was also performed on the experimental data.

Source: Marian Wiercigroch.

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Last Updated: 8th August 2002.