Asymptotic Methods for Relaxation Oscillations and Applications
Springer-Verlag New York Inc.
978-0-387-96513-0 (ISBN)
1. Introduction.- 1.1 The Van der Pol oscillator.- 1.2 Mechanical prototypes of relaxation oscillators.- 1.3 Relaxation oscillations in physics and biology.- 1.4 Discontinuous approximations.- 1.5 Matched asymptotic expansions.- 1.6 Forced oscillations.- 1.7 Mutual entrainment.- 2 Free oscillation.- 2.1 Autonomous relaxation oscillation: definition and existence.- 2.2 Asymptotic solution of the Van der Pol equation.- 2.3 The Volterra-Lotka equations.- 2.4 Chemical oscillations.- 2.5 Bifurcation of the Van der Pol equation with a constant forcing term.- 2.6 Stochastic and chaotic oscillations.- 3. Forced oscillation and mutual entrainment.- 3.1 Modeling coupled oscillations.- 3.2 A rigorous theory for weakly coupled oscillators.- 3.3 Coupling of two oscillators.- 4. The Van der Pol oscillator with a sinusoidal forcing term.- 4.1 Qualitative methods of analysis.- 4.2 Asymptotic solution of the Van der Pol equation with a moderate forcing term.- 4.2 Asymptotic solution of the Van der Pol equation with a large forcing term.- 4.3 Asymptotic solution of the Van der Pol equation with a large forcing term.- Appendices.- A: Asymptotics of some special functions.- B: Asymptotic ordering and expansions.- C: Concepts of the theory of dynamical systems.- D: Stochastic differential equations and diffusion approximations.- Literature.- Author Index.
Erscheint lt. Verlag | 3.4.1987 |
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Reihe/Serie | Applied Mathematical Sciences ; 63 |
Zusatzinfo | 4 Illustrations, black and white; XIII, 227 p. 4 illus. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika | |
Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
ISBN-10 | 0-387-96513-0 / 0387965130 |
ISBN-13 | 978-0-387-96513-0 / 9780387965130 |
Zustand | Neuware |
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