Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-07-07
Nonlinear Sciences
Exactly Solvable and Integrable Systems
36 pages, 6 figures. This is an elaborated presentation of my outlook on some concepts and problems of modern system theory wh
Scientific paper
The suggestion of writing, for some problems, nonlinear state equations not as dx/dt = F(x,u,t), but as dx/dt = [A(t,x)]x + [B(t,x)]u(t), which is more "constructive", is considered supported by arguments related to: the axiomatization of system theory, the classification of switched circuits as linear and nonlinear, the use of nonlinear sampling for measuring frequency without clock, the consideration of an ensemble of colliding particles in which the establishing of the chaotic movements is seen as a result of the same kind of nonlinearity as in electronic switching circuits, the modeling of a liquid medium as a "system" whose structure is directly influenced by the "input", and some other problems.
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