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Systems with sub-processes evolving on many different time scales
are ubiquitous in applications: chemical reactions, electro-optical
and neuro-biological systems, to name just a few. This volume
contains papers that expose the state of the art in mathematical
techniques for analyzing such systems. Recently developed geometric
ideas are highlighted in this work that includes a theory of
relaxation-oscillation phenomena in higher dimensional phase
spaces. Subtle exponentially small effects result from singular
perturbations implicit in certain multiple time scale systems.
Their role in the slow motion of fronts, bifurcations, and jumping
between invariant tori are all explored here. Neurobiology has
played a particularly stimulating role in the development of these
techniques and one paper is directed specifically at applying
geometric singular perturbation theory to reveal the synchrony in
networks of neural oscillators.
Systems with sub-processes evolving on many different time scales
are ubiquitous in applications: chemical reactions, electro-optical
and neuro-biological systems, to name just a few. This volume
contains papers that expose the state of the art in mathematical
techniques for analyzing such systems. Recently developed geometric
ideas are highlighted in this work that includes a theory of
relaxation-oscillation phenomena in higher dimensional phase
spaces. Subtle exponentially small effects result from singular
perturbations implicit in certain multiple time scale systems.
Their role in the slow motion of fronts, bifurcations, and jumping
between invariant tori are all explored here. Neurobiology has
played a particularly stimulating role in the development of these
techniques and one paper is directed specifically at applying
geometric singular perturbation theory to reveal the synchrony in
networks of neural oscillators.
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