By David John Warwick Simpson
Real-world platforms that contain a few non-smooth swap are frequently well-modeled through piecewise-smooth platforms. even though there nonetheless stay many gaps within the mathematical concept of such platforms. This doctoral thesis provides new effects relating to bifurcations of piecewise-smooth, non-stop, self sufficient platforms of standard differential equations and maps. a number of codimension-two, discontinuity triggered bifurcations are opened up in a rigorous demeanour. numerous 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; specifically, 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 complete history part is very easily supplied for people with very little event in piecewise-smooth platforms.
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