Multiple-Time-Scale Dynamical Systems

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.Additional ISBNs0387951261, 1461265290, 9780387951263, 9781461265290Multiple-Time-Scale Dynamical Systems 1st Edition is written by Alexander I. Khibnik; Christopher K. R. T. Jones and published by Springer. ISBNs for Multiple-Time-Scale Dynamical Systems are 9781461301172, 1461301173 and the print ISBNs are 9781461301172, 1461301173. Additional ISBNs include 0387951261, 1461265290, 9780387951263, 9781461265290.