@article{418205,
      note = {Originally presented as: Thesis (Ph.D.)--University of  Colorado at Boulder, 2008.},
      author = {Simpson, David John Warwick.},
      url = {http://library.usi.edu/record/418205},
      title = {Bifurcations in piecewise-smooth continuous systems  [electronic resource] /},
      publisher = {World Scientific,},
      abstract = {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.},
      recid = {418205},
      pages = {xv, 238 p. :},
      address = {New Jersey :},
      year = {2010},
}