Mechanical and neural oscillators with time delays

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This project is motivated by some specific biological and mechanical systems: the pupil light reflex, brain neural networks and metal cutting. Although physically unrelated, the behaviour of these systems is influenced by the same factors: the presence of nonlinearities and time delays. The time delays represent the time it takes information to propagate from one part of the system to another. The nonlinearity represents the fact that in these systems a small change in the state can often result in a large change in behaviour. An oscillator is any object that performs a repetitive motion. A familiar example is the pendulum of a clock. This project considers several oscillators which fall into two themes, based on how they are modelled mathematically.