By David John Warwick Simpson
Real-world platforms that contain a few non-smooth swap are usually well-modeled by way of piecewise-smooth platforms. despite the fact that there nonetheless stay many gaps within the mathematical conception of such structures. This doctoral thesis provides new effects relating to bifurcations of piecewise-smooth, non-stop, self sustaining structures of standard differential equations and maps. a variety of codimension-two, discontinuity caused bifurcations are spread out in a rigorous demeanour. a number of of those unfoldings are utilized to a mathematical version of the expansion of Saccharomyces cerevisiae (a universal yeast). the character of resonance close to border-collision bifurcations is defined; particularly, the curious geometry of resonance tongues in piecewise-smooth non-stop maps is defined intimately. Neimark-Sacker-like border-collision bifurcations are either numerically and theoretically investigated. A accomplished historical past part is very easily supplied for people with very little adventure in piecewise-smooth structures.
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