Issues‎ > ‎vol17n3‎ > ‎

Floquet Theory for Stability of Differential Algebraic Equations.


Kamal. H. Yasir1 , Hassan. Sh.Kadem2

1 Department of Mathematics, College of Computer Sciences and Mathematics,Thi-Qar University, Thi-Qar, Iraq.
2 Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University, Thi-Qar, Iraq


Abstract
Motivated by a great useful of some types of non autonomous differential algebraic
equation systems ( so called strangeness free ) and its applied in different scientific
fields, we present several new results for studying such systems by classical Floquet
Theory, which we extended from linear periodic ordinary differential equation systems
into linear periodic differential algebraic equation systems. For both systems we
investigate that they have the same Floquet exponents. The relation between monodromy
matrices of both systems is also presented. Classification of solution according to the
nature of Floquet exponent is established. Then according to these results, we study the
stability and bifurcation phenomenon of our differential algebraic equation systems.

Key Words: Differential lgebraic equation Floquet theory stability bifurcation



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