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Stability in the models of real world phenomena. (English) Zbl 1283.70006
From the text: In this paper the author considers several examples of real world models to illustrate the general methods of stability analysis of nonlinear systems developed recently in the Department of Stability of Processes of S. P. Timoshenko Institute of Mechanics of NAS of Ukraine and in the books of the author et al.
Section 2 deals with the stability of robot motion whose mathematical model takes into account the dynamics of the environment interacting with the robot. Here some integral inequalities from Chapter 1 of the book [V. Lakshmikantham, S. Leela and the author, Stability analysis of nonlinear systems. New York etc.: Marcel Dekker (1989; Zbl 0676.34003)] are applied.
In Section 3, he considers neural networks on time scales and introduces the study of the stability problem in this new direction. In Section 4, he considers a problem of stability of regular synchronous generator of optical connected lasers.
In Section 5 he presents models from economics and using the method of vector Lyapunov functions he proves that a market tends to some given evolution independent of initial conditions. Finally in Section 6, he analyzes a model of impulsive Takagi-Sugeno systems with application to the mathematical model in population growth under impulsive control.
{Editorial remark: In the original the author’s name is mistakenly listed as A. A. Martunyuk.}

MSC:
70E60 Robot dynamics and control of rigid bodies
70E50 Stability problems in rigid body dynamics
34D20 Stability of solutions to ordinary differential equations
34N05 Dynamic equations on time scales or measure chains
78A60 Lasers, masers, optical bistability, nonlinear optics
91B62 Economic growth models
93C42 Fuzzy control/observation systems
93D30 Lyapunov and storage functions
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