| Title:
|
On weak non-linearity of models of physical systems (English) |
| Author:
|
Mayer, Daniel |
| Author:
|
Ryjáček, Zdeněk |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
22 |
| Issue:
|
4 |
| Year:
|
1977 |
| Pages:
|
301-310 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The introduction of the concept of weak non-linearity is motivated by the effort to determine a certain class of non-linear systems whose properties important in technical appliations coincide with those of asymptotically stable linear systems. A model of the phzsical system described by Eq. (1) is called weakly non-linear (quasilinear) if any two solutions $x_1(t), x_2(t)$ of Eq. (1) sarisfy Eq. (2). A model described by Eq. (1) is weakly non-linear if there exists a way of expressing the right-hand side $f(x,t)$ of this equation in the form (3) so that the inequality (8) is satisfied. () |
| MSC:
|
34A99 |
| MSC:
|
34D20 |
| idZBL:
|
Zbl 0373.34028 |
| idMR:
|
MR0441043 |
| DOI:
|
10.21136/AM.1977.103705 |
| . |
| Date available:
|
2008-05-20T18:07:45Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103705 |
| . |
| Reference:
|
[1] D. Mayer: Numerical steady-state of weakly nonlinear systems with periodic inputs.Acta Technica ČSAV, 1977, No. 3. |
| Reference:
|
[2] D. Mayer: Formulating state equations of electric networks by a simple method.Acta Technica ČSAV, 1975, No. 3, 275-300. Zbl 0306.94025, MR 0389431 |
| Reference:
|
[3] N. Balabanian T. A. Bickart: Electrical Network Theory.New York, J. Willey, 1969. |
| Reference:
|
[4] D. Mayer: An Introduction to the Theory of Electric Networks.Praha, SNTL, 1978 (Czech; in print). |
| Reference:
|
[5] Ph. Hartmann: Ordinary Differential Equations.New York, J. Wiley, 1964. MR 0171038 |
| Reference:
|
[6] Z. Kotek S. Kubík M. Razím: Non-Linear Dynamical Systems.Praha, SNTL, 1973 (Czech). |
| Reference:
|
[7] M. lkeda S. Kodama: Large-Scale Dynamical Systems: State Equations, Lipschitz Conditions, and Linearization.IEEE Transaction on Circuit Theory, Vol. CT-20, No. 3, 1973, 193 - 202. MR 0368840, 10.1109/TCT.1973.1083656 |
| . |
