Floquet Theory for Stability of Differential Algebraic Equations

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
E-mail: istathj@yahoo.com
E-mail: Mhamed Alsalhi@yahoo.com


Article info

Original: 24 Jan. 2015
Revised: 22 Mar. 2015
Accepted: 19 Apr. 2015
Published online:   20 Sep. 2015           





Key Words:
Differential lgebraic equation
Floquet theory
stability 
bifurcation     
   



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.





Ċ
Kewan Omer,
Sep 20, 2015, 9:45 AM