Floquet Theory for Stability of Differential Algebraic Equations.

Volume 17 , Issue 3 , September 2015 , Pages 73-86

Authors

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

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.

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