Author | Grasman, Johan. author |
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Title | Asymptotic Methods for Relaxation Oscillations and Applications [electronic resource] / by Johan Grasman |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1987 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1056-6 |
Descript | XIII, 227 p. 4 illus. online resource |
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