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Noise-induced transitions: Theory and applications in physics, chemistry and biology

Noise-induced transitions: Theory and applications in physics, chemistry and biology Acta Applicandae Mathematicae 11 (1988) 97 Book Reviews W. Horsthemke and R. Lefever: Noise-Induced Transitions: Theory and Ap- plications in Physics, Chemistry and Biology, Springer-Verlag, Berlin, 1984. The subject matter of this book belongs to an area of applications of mathematics to very diverse fields of natural (and social) sciences, probably as large as the field of applications of differential equations. This being so mainly because the problems dealt with arise by 'adding noise' to the equations that are used to model the dynamics of the system under study. But the aim of the book is not to study the stochastic differential equations used to model systems under the action of a random environment, its goal being instead to study the dependence of the equilibrium distribution on the parameters of the system. When a system is subjected to a random environment, its state is no longer a point in a phase (or state) space, but a measure: the probability distribution of the random variable describing the instantaneous, random, state of the system. These probability distributions change in time according to equations naturally asso- ciated with the problem. The equilibrium distributions being the time in- dependent solutions of these evolution http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Noise-induced transitions: Theory and applications in physics, chemistry and biology

Gzyl, Henryk
Acta Applicandae Mathematicae , Volume 11 (1) – May 3, 2004
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References (4)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00047115
Publisher site
See Article on Publisher Site

Abstract

Acta Applicandae Mathematicae 11 (1988) 97 Book Reviews W. Horsthemke and R. Lefever: Noise-Induced Transitions: Theory and Ap- plications in Physics, Chemistry and Biology, Springer-Verlag, Berlin, 1984. The subject matter of this book belongs to an area of applications of mathematics to very diverse fields of natural (and social) sciences, probably as large as the field of applications of differential equations. This being so mainly because the problems dealt with arise by 'adding noise' to the equations that are used to model the dynamics of the system under study. But the aim of the book is not to study the stochastic differential equations used to model systems under the action of a random environment, its goal being instead to study the dependence of the equilibrium distribution on the parameters of the system. When a system is subjected to a random environment, its state is no longer a point in a phase (or state) space, but a measure: the probability distribution of the random variable describing the instantaneous, random, state of the system. These probability distributions change in time according to equations naturally asso- ciated with the problem. The equilibrium distributions being the time in- dependent solutions of these evolution

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Acta Applicandae Mathematicae – Springer Journals

Published: May 3, 2004

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