Download E-books Bifurcations in Piecewise-smooth Continuous Systems (World Scientific Series on Nonlinear Science Series a) (Volume 70) PDF

By David John Warwick Simpson

Real-world structures that contain a few non-smooth swap are frequently well-modeled via piecewise-smooth platforms. even though there nonetheless stay many gaps within the mathematical thought of such platforms. This doctoral thesis offers new effects relating to bifurcations of piecewise-smooth, non-stop, self sufficient structures of normal differential equations and maps. numerous 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; 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 entire heritage part is comfortably supplied for people with very little event in piecewise-smooth structures.

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