Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description. This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory. The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems. In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.
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Readership: Graduate students and researchers in nonlinear science and chaos theory; electrical and electronic engineers; experts in control theory and in applied mathematics.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
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In a most surprising manner, modern theory of nonlinear dynamics has disclosed a number of misconceptions in our understanding of the laws of motion. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
time deadzone, swallow tail structure, relay feedback systems, arises softly, relay control systems, piecewise smooth systems, torus destruction, relay element, resonance torus, resonance cycles, skew tent map, resonance tongues, nonlinear dynamic phenomena, collision bifurcations, new torus, saddle cycle, beer model, hysteretic transitions, chaotic intervals, bifurcation boundaries, unstable cycles, quasiperiodic behavior, economic long wave, quasiperiodic oscillations, chaotic oscillations Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, World Scientific, Circuits Syst, Nonlinear Oscillations, Theory Appl, Elsevier Science, Springer Verlag, Discrete Dynamics, Electrical Technology, Forced Oscillations, Kluwer Academic Publ, Nauka Publ, Nauka Puhl, Discontinuous Nonlinearities, Sound Vihr, Stochastic Features, Buck Converter, Industrial Dynamics, Modulating Power Supplies of Radioelectronic Devices, Period Three, Plenum Publishing, Sloan School of Management, Switch-Mode Power Supply Design New!
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
In a most surprising manner, modern theory of nonlinear dynamics has disclosed a number of misconceptions in our understanding of the laws of motion. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
time deadzone, swallow tail structure, relay feedback systems, arises softly, relay control systems, piecewise smooth systems, torus destruction, relay element, resonance torus, resonance cycles, skew tent map, resonance tongues, nonlinear dynamic phenomena, collision bifurcations, new torus, saddle cycle, beer model, hysteretic transitions, chaotic intervals, bifurcation boundaries, unstable cycles, quasiperiodic behavior, economic long wave, quasiperiodic oscillations, chaotic oscillations Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, World Scientific, Circuits Syst, Nonlinear Oscillations, Theory Appl, Elsevier Science, Springer Verlag, Discrete Dynamics, Electrical Technology, Forced Oscillations, Kluwer Academic Publ, Nauka Publ, Nauka Puhl, Discontinuous Nonlinearities, Sound Vihr, Stochastic Features, Buck Converter, Industrial Dynamics, Modulating Power Supplies of Radioelectronic Devices, Period Three, Plenum Publishing, Sloan School of Management, Switch-Mode Power Supply Design New!
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 42
books:
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- Industrial Dynamics by Jay Wright Forrester on page 66, page 321, and Back Matter
- Modern Power Electronics by B.K. Bose on page 159, page 228, and page 274
- Chaos in Dynamical Systems by Edward Ott on page 58, page 87, and page 110
- Power Electronics: Converters, Applications and Design by Ned Mohan on page 164, page 228, and page 274
- Switch-Mode Power Supply Design by P. R. K. Chetty on page 164, page 228, and page 274
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