Mathematical modelling is ubiquitous. Almost every book in exact science
touches on mathematical models of a certain class of phenomena, 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 non-linear dynamics and mathematical
modelling from discrete sequences of experimental measurements (time
series). The latter direction of research is known 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, non-stationary and noise-corrupted signals which
are typical of real-world objects and phenomena) with relatively simple
non-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 non-trivial solutions that promise
suf?ciently simple modelling of complex processes; according to the
concepts of non-linear dynamics, chaotic regimes can be demonstrated
already by a third-order non-linear ordinary differential equation,
while complex behaviour in a linear model can be induced either by
random in?uence (noise) or by a very high order of equations.
