Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable models for further mathematical analysis or computer simulations. For the most part, derivations are based on perturbation methods, and the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro-differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added.
Analysis and Simulation of Chaotic Systems
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Key Phrases - Statistically Improbable Phrases (SIPs):
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rotation vector method, regular perturbation theorem, oscillatory matrix, quasistatic state, stability under persistent disturbances, modified perturbation method, unique periodic solution, averaging theorem, quasistatic problem, cusp surface, quasiperiodic function, bifurcation equations, nonlinear stability analysis, return mapping, averaged system, orbital stability, singular perturbation problems, characteristic multipliers, rotation number, small divisors, invariant torus, small positive parameter, stable matrix, perturbed problem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hamilton Jacobi, Fredholm's Alternative, Euler Lagrange, Initial Transient Theorem, No-Retract Theorem, Nonresonance Theorem, Systems of Two Equations, Twist Theorem, Averaging Systems, Oscillations of Equations New!
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rotation vector method, regular perturbation theorem, oscillatory matrix, quasistatic state, stability under persistent disturbances, modified perturbation method, unique periodic solution, averaging theorem, quasistatic problem, cusp surface, quasiperiodic function, bifurcation equations, nonlinear stability analysis, return mapping, averaged system, orbital stability, singular perturbation problems, characteristic multipliers, rotation number, small divisors, invariant torus, small positive parameter, stable matrix, perturbed problem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hamilton Jacobi, Fredholm's Alternative, Euler Lagrange, Initial Transient Theorem, No-Retract Theorem, Nonresonance Theorem, Systems of Two Equations, Twist Theorem, Averaging Systems, Oscillations of Equations New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 100
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- Perturbation Methods in Applied Mathematics (Applied Mathematical Sciences) by J. Kevorkian in Front Matter, Back Matter (1), and Back Matter (2)
- Partial Differential Equations: Analytical Solution Techniques (Texts in Applied Mathematics) by J. Kevorkian in Front Matter, and Back Matter
- Weakly Connected Neural Networks by Frank C. Hoppensteadt in Back Matter (1), and Back Matter (2)
- Sturmian Theory for Ordinary Differential Equations (Applied Mathematical Sciences) by William T. Reid in Front Matter
- Lectures on Viscoelasticity Theory (Applied Mathematical Sciences) by A.C. Pipkin in Front Matter
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- Nonlinear Problems of Elasticity (Applied Mathematical Sciences) by Stuart Antman in Back Matter (1), and Back Matter (2)
- Turbulent Flow Computation (Fluid Mechanics and Its Applications) by D. Drikakis on page 232
- Stability by Liapunov's Matrix Function Method with Applications (Pure and Applied Mathematics) (Chapman & Hall/CRC Pure and Applied Mathematics) by A.A. Martynyuk in Back Matter
- Multiple Scale and Singular Perturbation Methods (Applied Mathematical Sciences) by J.K. Kevorkian in Back Matter
- Dynamics in Infinite Dimensions by Jack K. Hale in Back Matter
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