Publisher's 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.
