Titre :	Les systémes chaotiques à dérivées fractionnaires
Type de document :	texte imprimé
Auteurs :	Mohammed-Salah Abdelouahab, Auteur ; N. Hamri, Directeur de thèse
Editeur :	constantine [Algérie] : Université Constantine 1
Année de publication :	2013
Importance :	119 f.
Format :	30 cm.
Note générale :	2 copies imprimées disponibles
Langues :	Français (fre)
Catégories :	Français - Anglais Mathématiques
Tags :	Fractional-order dérivatives  Stability of fractional-order systems  Bi- furcation  Periodic solutions  Chaos  Chaos control  D´eriv´ees d’ordre fractionnaire  Stabilit´e des syst`emes d’ordre frac-tionnaire  Bifurcation  Solutions p´eriodiques  Contrˆole du chaos  النظم ذات المشتقات الكسرية  استقرار النظم الكسرية  التفرع  الحلول الدورية الشواش  التحكم في الشواش
Index. décimale :	510 Mathématiques
Résumé :	This thesis deals with fractional-order chaotic systems. The main highlight is on some basic differences between a fractional-order system and its integer order counterpart. Namely, stability conditions, existence of periodic solutions and min-imal total order for which chaos can occur etc... The finding of a new chaotic attractor from Hybrid optical bistable system is reported and dynamic of the new system is investigated in both integer and fractional-order cases. It is shown that asymptotic stability of equilibrium points of the fractional system can occur with positive real part of some corresponding eigenvalues which is not the case in integer-order systems. We have established criterion under which a fractional-order system undergoes Hopf bifurcation. The results are validated by mean of stability theory and numerical simulations. It is shown that chaos can be occurred in fractional-order system with total order less than three which is not the case in integer-order system due to the Poincar´e- Bendixon theorem. Finally, nonlinear feedback control scheme has been extended to control fractional financial system. The results are proved analytically by applying the stability condition for fractional system. Numerically the unstable fixed points have been successively stabilized for different values of fractional order; moreover some un-stable periodic orbits have been stabilized.
Diplôme :	Doctorat en sciences
En ligne :	../theses/math/ABD6412.pdf
Format de la ressource électronique :	pdf
Permalink :	https://bu.umc.edu.dz/md/index.php?lvl=notice_display&id=9437

Les systémes chaotiques à dérivées fractionnaires [texte imprimé] / Mohammed-Salah Abdelouahab, Auteur ; N. Hamri, Directeur de thèse . - constantine [Algérie] : Université Constantine 1, 2013 . - 119 f. ; 30 cm.
2 copies imprimées disponibles
Langues : Français (fre)

Catégories :	Français - Anglais Mathématiques
Tags :	Fractional-order dérivatives  Stability of fractional-order systems  Bi- furcation  Periodic solutions  Chaos  Chaos control  D´eriv´ees d’ordre fractionnaire  Stabilit´e des syst`emes d’ordre frac-tionnaire  Bifurcation  Solutions p´eriodiques  Contrˆole du chaos  النظم ذات المشتقات الكسرية  استقرار النظم الكسرية  التفرع  الحلول الدورية الشواش  التحكم في الشواش
Index. décimale :	510 Mathématiques
Résumé :	This thesis deals with fractional-order chaotic systems. The main highlight is on some basic differences between a fractional-order system and its integer order counterpart. Namely, stability conditions, existence of periodic solutions and min-imal total order for which chaos can occur etc... The finding of a new chaotic attractor from Hybrid optical bistable system is reported and dynamic of the new system is investigated in both integer and fractional-order cases. It is shown that asymptotic stability of equilibrium points of the fractional system can occur with positive real part of some corresponding eigenvalues which is not the case in integer-order systems. We have established criterion under which a fractional-order system undergoes Hopf bifurcation. The results are validated by mean of stability theory and numerical simulations. It is shown that chaos can be occurred in fractional-order system with total order less than three which is not the case in integer-order system due to the Poincar´e- Bendixon theorem. Finally, nonlinear feedback control scheme has been extended to control fractional financial system. The results are proved analytically by applying the stability condition for fractional system. Numerically the unstable fixed points have been successively stabilized for different values of fractional order; moreover some un-stable periodic orbits have been stabilized.
Diplôme :	Doctorat en sciences
En ligne :	../theses/math/ABD6412.pdf
Format de la ressource électronique :	pdf
Permalink :	https://bu.umc.edu.dz/md/index.php?lvl=notice_display&id=9437