Multiple parameter stability theory and its applications : bifurcations, catastrophes, instabilities, ...
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Bibliographic Information
Multiple parameter stability theory and its applications : bifurcations, catastrophes, instabilities, ...
（The Oxford engineering science series, 18）
Clarendon Press , Oxford University Press, c1986
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Note
Bibliography: p. [270]-278
Includes index
Description and Table of Contents
Description
In this book, a general non-linear theory concerning the stability, instability, bifurcation, and oscillatory behaviour of autonomous systems is presented from an original engineering point of view which is conceptually simple and applicable. The emphasis is on analytical procedures which lead to construction of asymptotic solutions. Potential systems, which can only exhibit static instabilities, are treated separately. Various bifurcation phenomena and the associated imperfection-sensitivities are analysed via the multiple-parameter perturbation technique. The method leads to 'elementary catastrophes'. The emphasis, however, is on non-potential systems which may exhibit dynamic as well as static instability phenomena. This requires a new formulation which is capable of yielding information concerning periodic solutions. Thus, an intrinsic harmonic balancing technique is introduced for the analysis of the dynamic bifurcations, which parallels that of the equilibria. The approach leads to a unified treatment of both static and dynamic bifurcation phenomena within an autonomous framework.
Table of Contents
- Introduction : Introductory remarks
- Classification of systems
- Basic concepts, definitions and stability criteria. Static Criteria : Potential systems
- One-parameter autonomous systems
- Multiple-parameter autonomous systems. Dynamic instability : Fundamentals
- One-parameter systems
- Multiple-parameter systems
- Chaotic motions. Applications : Mechanics and structural systems
- Electrical networks
- A Mathematical model
- Hopf bifurcation
- Gyroscopic systems
- Bifurcations in biochemical processes
- Thermodynamics and phase transition
- Evolution of ecosystems
- Population dynamics
- Evolutionary processes in socio-economic systems
- Human systems.
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