Geodesic
On weak non-linearity of models of physical systems
Applications of Mathematics, Tome 22 (1977) no. 4, pp. 301-310
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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.
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.
DOI : 10.21136/AM.1977.103705
Classification : 34A99, 34D20 
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Mayer, Daniel; Ryjáček, Zdeněk. On weak non-linearity of models of physical systems. Applications of Mathematics, Tome 22 (1977) no. 4, pp. 301-310. doi: 10.21136/AM.1977.103705

[1] D. Mayer: Numerical steady-state of weakly nonlinear systems with periodic inputs. Acta Technica ČSAV, 1977, No. 3.

[2] D. Mayer: Formulating state equations of electric networks by a simple method. Acta Technica ČSAV, 1975, No. 3, 275-300. | MR | Zbl

[3] N. Balabanian T. A. Bickart: Electrical Network Theory. New York, J. Willey, 1969.

[4] D. Mayer: An Introduction to the Theory of Electric Networks. Praha, SNTL, 1978 (Czech; in print).

[5] Ph. Hartmann: Ordinary Differential Equations. New York, J. Wiley, 1964. | MR

[6] Z. Kotek S. Kubík M. Razím: Non-Linear Dynamical Systems. Praha, SNTL, 1973 (Czech).

[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. | DOI | MR

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