Embedded Files
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
DOI: https://doi.org/10.17656/jzs.10402
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
References
[1] Cutsem.T.V.,”Voltage instability: Phenomena, countermeasures, and analysis methods”
Proceedings of the IEEE, vol. 88, Issue 2, pp. 208-227, Feb. (2000.)
[2] Lawrence P.“Differential Equations and Dynamical Systems”,Third addition, Springerverlag, USA,
(2001.)
[3] Jianjun P. “New Results in Floquet theory”, Department of Mathematics. The College of William
and Mary Williamsburg, VA 23187, USA, (2003).
[4]Vorgelegt V., “ Linear Differential-Algebraic Equations of Higher-Order and the Regularity
orSingularity of Matrix Polynomials”, Dipl.-Math. Chunchao Shi von der Fakultat II –Mathematikund
Naturwissenschaften der TechnischenUniversitat Berlin zurErlangung des akademischenGrades,Berlin,
( 2004).
[5] Alexandra D. and S.c. Sinha.., “Bifurcation Analysis of Nonlinear Dynamic Systems withTime-
Periodic Coefficients”,Nonlinear Systems Research Laboratory,Department of MechanicalEngineering,
Auburn University,202 Ross Hall, Auburn, AL 36849, USA, (2006).
[6] 1M. Sahadet H. and 2M. Mosta_zur R.,”linear differential algebraic equations withconstant
coefficients” 1Deparment of Mathematics, Chemnitz University of Technology, Germany and
2Department of Information Engineering and Science, University of Trento, Trento,Italy.July, (2009.)
[7]Thomas B.“On stability of time-varying linear differential-algebraic equations”,Technische
UniversitatIlmenau, 22.02, (2010)
[8] Vu Hoang L.,“spectral analysis for linear differential algebraic equations”, Faculty of Mathematics,
Mechanics and Informatics Vietnam National University 334, Nguyen Trai Str., Thanh Xuan,
Hanoi,Vietnam Volker MehrmannInstitut fur Mathematik, MA 4-5 Technische Universitat Berlin D-
10623 Berlin, Fed. Rep. Germany, (2011.)
[9] Ernst H.,“Solving Differential Equations on Manifolds”, University of Reodiganero, June, (2011.)
[10]Thomas B., and Achim Ilchman.“On stability of time-varying linear differential algebraic
equations”,Institute for mathematics, Ilmenau, University of technology, Germany, 31 January, (2013.)
[11] Eich-Soellner, E., and F ̈uhrer, C.,”Numerical methods in multibody dynamics” Stuttgart:
Teubner,(1998).
[12] Riaza, R.,”Differential-algebraic systems. Analytical aspects and circuit applications” World
Scientific Basel: Publishing, (2008).
[13] Kumar, A., and Daoutidis, P.,” Control of nonlinear differential algebraic equation systems with
applications to chemical processes” volume 397 of Chapman and Hall/CRC research notes in
mathematics. Boca Raton: Chapman and Hall, (1999).
[14]Ilchmann, A., and Mehrmann, V., “A behavioral approach to time-varying linear systems, Part 1:
General theory”SIAM Journal on Control and Optimization, 44(5), 1725–1747. (2005a).
Page updated
Report abuse