Mathematical modelling is ubiquitous. Almost every book in exact science touches on mathematical models of a certain class of phemena, on more or less speci?c approaches to construction and investigation of models, on their applications, etc. As many textbooks with similar titles, Part I of our book is devoted to general qu- tions of modelling. Part II re?ects our professional interests as physicists who spent much time to investigations in the ?eld of n-linear dynamics and mathematical modelling from discrete sequences of experimental measurements (time series). The latter direction of research is kwn for a long time as system identi?cation in the framework of mathematical statistics and automatic control theory. It has its roots in the problem of approximating experimental data points on a plane with a smooth curve. Currently, researchers aim at the description of complex behaviour (irregular, chaotic, n-stationary and ise-corrupted signals which are typical of real-world objects and phemena) with relatively simple n-linear differential or difference model equations rather than with cumbersome explicit functions of time. In the second half of the twentieth century, it has become clear that such equations of a s- ?ciently low order can exhibit n-trivial solutions that promise suf?ciently simple modelling of complex processes; according to the concepts of n-linear dynamics, chaotic regimes can be demonstrated already by a third-order n-linear ordinary differential equation, while complex behaviour in a linear model can be induced either by random in?uence (ise) or by a very high order of equations.
Boris P. Bezruchko, Dmitry A. Smirnov
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Date of Publication
Springer Series in Synergetics
Place of Publication
Country of Publication
Springer-Verlag Berlin and Heidelberg GmbH & Co. K