Stability and instability for dynamic equations on time scales
| Autor: | Joan Hoffacker, Christopher C. Tisdell |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Dynamic system of equations
Invariance principle Mathematical analysis Instability Scale (descriptive set theory) Positive-definite matrix Time scales Stability (probability) Computational Mathematics Compact space Computational Theory and Mathematics Modeling and Simulation Modelling and Simulation Liapunov function Stability Dynamic equation Mathematics Sign (mathematics) |
| Zdroj: | Computers & Mathematics with Applications. 49(9-10):1327-1334 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2005.01.016 |
| Popis: | In this paper we examine the stability and instability of the equilibrium solution x = 0 to the first-order system of dynamic equations x^@D=f(t,x),t>=t"0,x@?D@?R^n,where t is from a so-called time scale T with t"0 @? Tand D is a compact set. Our methods involve the existence of a positive definite Liapunov function V, such that its delta-derivative V^@D satisfies certain integral, definite or semidefinite sign properties. Finally, we use Liapunov functions to develop an invariance principle regarding solutions to the above dynamic equation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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