| Description |
1 online resource (xv, 238 pages) : illustrations (some color) |
| Series |
World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70 |
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World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 70.
|
| Contents |
Preface; Acknowledgments; Contents; 1. Fundamentals of Piecewise-Smooth, Continuous Systems; 2. Discontinuous Bifurcations in Planar Systems; 3. Codimension-Two, Discontinuous Bifurcations; 4. The Growth of Saccharomyces cerevisiae; 5. Codimension-Two, Border-Collision Bifurcations; 6. Periodic Solutions and Resonance Tongues; 7. Neimark-Sacker-Like Bifurcations; Appendix A Selected Proofs; Appendix B Additional Figures; Appendix C Adjugate Matrices; Appendix D Parameter Values for S. cerevisiae; Bibliography; Index |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Bifurcation theory.
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Differential equations.
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Saccharomyces cerevisiae.
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Saccharomyces cerevisiae
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MATHEMATICS -- Differential Equations -- General.
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Bifurcation theory
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Differential equations
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Saccharomyces cerevisiae
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| Form |
Electronic book
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| LC no. |
2010484011 |
| ISBN |
9789814293853 |
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9814293857 |
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1282763423 |
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9781282763425 |
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9786612763427 |
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6612763426 |
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