This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical
models of such multiple-scale systems are considered singular perturbation problems and this
volume focuses on the geometric approach known as Geometric Singular Perturbation Theory
(GSPT).It is the first of its kind that introduces the GSPT in a coordinate-independent manner.
This is motivated by specific examples of biochemical reaction networks electronic circuit and
mechanic oscillator models and advection-reaction-diffusion models all with an inherent
non-uniform scale splitting which identifies these examples as singular perturbation problems
beyond the standard form. The contents cover a general framework for this GSPT beyond the
standard form including canard theory concrete applications and instructive qualitative
models. It contains many illustrations and key pointers to the existing literature. The target
audience are senior undergraduates graduate students and researchers interested in using the
GSPT toolbox in nonlinear science either from a theoretical or an application point of view.
Martin Wechselberger is Professor at the School of Mathematics & Statistics University of
Sydney Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial
and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple
time-scales.
