Oscillatory Evolution Processes: Quantitative Analyses Arising from Applied Science (Nonlinear Science : Theory and Applications) - Hardcover

Gumowski, F.

Hardcover

ISBN 10: 0719022126 ISBN 13: 9780719022128

Publisher: Manchester University Press, 1989

Synopsis

Nonlinear Science Theory and Applications Series editor Arun V. Holden Centre for Nonlinear Studies, University of Leeds Oscillatory evolution processes I. Gumowski This guide to the use of evolution equations in modelling the behaviour of real systems, and the analysis of experimental results will be a significant help to the many workers in empirical sciences who find it difficult to connect the abstractions of much modern nonlinear mathematical theory to their work. A study of oscillatory evolution processes that is useful in practical applications requires not only a realistic mathematical formulation or model, followed by a qualitative analysis of what might possibly happen independently of its quantitative scale, but also analytic expressions describing the evolving variables as functions of time. These can provide explicit quantitative relations between the parameters appearing in the model and the parameters of the oscillatory wave forms, which allows a critical comparison of theoretical and experimental data. A construction of quantitatively accurate oscillatory solutions demonstrates that many apparently chaotic evolution processes have intrinsic regularities. This is illustrated using examples drawn from actual applications for second order nonlinear ordinary differential equations with periodic coefficients, and for third and fourth order autonomous differential equations.

Edition details

• Publisher: Manchester University Press
• Publication date: 1989
• Language: English
• ISBN 10: 0719022126
• ISBN 13: 9780719022128
• Binding: Hardcover
• Number of pages: 240