Laika skalu dinamisko vienādojumu integrālā stabilitāte
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Latvijas Universitāte
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Abstract
Darbā aplūkota laika skalu dinamisko vienādojumu integrālā stabilitāte. Apskatītas svarīgākās laika skalu īpašības, triviālā atrisinājuma stabilitātes jēdziens parastajiem diferenciālvienādojumiem, diferenču vienādojumiem un laika skalu vienādojumiem. Darba mērķis ir pierādīt dinamisko sistēmu stabilitāti izmantojot laika skalu analīzi, kas būtu
vispārīgs pierādījums, ko var reducēt gan uz parasto diferenciālvienādojumu stabilitāti, ja T = R, gan uz diferenču vienādojumu stabilitāti, ja T = Z, kur T ir laika skala.
In this thesis we investigate integral stability of dynamic systems on time scales. We define some important properties of time scales and definitions of the stability of ordinary differential equations, difference equations and equations on time scales. The aim of this work is to genaralize the reduction principle to the case of the dynamic systems on time scales and give the proof of stability on time scales, that can be reduced to stability of ordinary differential equations for T = R and to stability of difference equations for T = Z, where T is the time scale.
In this thesis we investigate integral stability of dynamic systems on time scales. We define some important properties of time scales and definitions of the stability of ordinary differential equations, difference equations and equations on time scales. The aim of this work is to genaralize the reduction principle to the case of the dynamic systems on time scales and give the proof of stability on time scales, that can be reduced to stability of ordinary differential equations for T = R and to stability of difference equations for T = Z, where T is the time scale.