Our website is made possible by displaying online advertisements to our visitors.
Please consider supporting us by disabling your ad blocker.

Download links will be available after you disable the ad blocker and reload the page.

Bifurcations in Piecewise-smooth Continuous Systems (World Scientific Series on Nonlinear Science Series a)



Description:

Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. Neimark-Sacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.

Download options:

Option 1 (added 2 months ago)
Option 2 (added 1 year ago)