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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.
References:
[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 0389431 | Zbl 0306.94025
[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 0171038
[6] Z. Kotek S. Kubík M. Razím: Non-Linear Dynamical Systems. Praha, SNTL, 1973 (Czech).
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