Titlebook: Asymptotic Methods for Relaxation Oscillations and Applications; Johan Grasman Book 1987 Springer-Verlag New York, Inc. 1987 Approximation

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0066-5452 ture: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation

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Paulo Carreira,Vasco Amaral,Hans Vangheluweoriginal position. In the applied sciences relaxation oscillations are most frequently met in biochemical and biological systems. A similar phenomenon is observed for these systems: during a short time interval of the cycle one or more components of the biological system may exhibit a fast change in their density.

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Free Oscillation, in detail. A similar asymptotic analysis of the Volterra-Lotka equations is made. We deal with Van der Pol oscillators with a stochastic and a constant forcing term and finally construct a chaotic relaxation oscillator.

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Forced Oscillation and Mutual Entrainment,or without delay. A rigorous theory for the existence of entrained solutions of systems without delays is given. Numerical solutions of the iteration mapping for the phase functions of the oscillators yields results that can be used for the interpretation of entrainment phenomena in biological syste