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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
MathématiquesTags : 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 : 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
MathématiquesTags : 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 : Permalink : https://bu.umc.edu.dz/md/index.php?lvl=notice_display&id=9437 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité ABD/6412 ABD/6412 Thèse Bibliothèque principale Thèses Disponible Documents numériques
texte intégraleAdobe Acrobat PDF
Titre : Analyse du chaos dans un système d’équations différentielles fractionnaires Type de document : texte imprimé Auteurs : Tarek Houmor, Auteur ; N. Hamri, Directeur de thèse Editeur : constantine [Algérie] : Université Constantine 1 Année de publication : 2014 Importance : 136 f. Format : 30 cm. Note générale : 2 copies imprimées disponibles
Langues : Français (fre) Catégories : Français - Anglais
MathématiquesTags : Dérivées d’ordre fractionnaire Chaos Exposants de Lyapounov Fer à cheval
topologique Test 0-1 Synchronisation du chaos Fractional-order derivatives Lyapounov exponent Topological horseshoe 0-1 test Chaos synchronization مشتقات ذات رتبة كسرية الفوضى قوى ليابونوف الحدوة الطوبولوجية الإختبار
1-0 التزامنIndex. décimale : 510 Mathématiques Résumé : In this thesis, we focus on the differential equations of fractional order systems exhibiting chaotic dynamics. Particular attention has been paid to a nonlinear system of fractional differential equations modeling the phenomenon of nuclear magnetic resonance : the Bloch system. A qualitative analysis of the dynamics of this system has been made, including some basic properties : bifurcations, periodic windows and routes to chaos. These properties were analyzed numerically by bifurcation diagram, phase portraits and Lyapunov exponents .
The chaotic behavior of this system was confirmed by the existence of a positive Lyapunov exponent.
On the other hand, the topological horseshoe was found, rigorously proving the chaotic nature of our system for certain parameter values, this method is considered as an excellent substitute for the Lyapunov spectrum method, less reliable numerically.
0-1 test provides a simple and efficient criterion for the distinction chaotic solutions of regular
orbits, we have successfully applied this test in our work.
Finally, the method of non-linear control was extended to realize the identical synchronization of two fractional Bloch systems. The results were proven analytically using stability conditions for fractional systems. A numerical simulation was performed to validate the results.Diplôme : Doctorat en sciences En ligne : ../theses/math/HOU6606.pdf Format de la ressource électronique : Permalink : https://bu.umc.edu.dz/md/index.php?lvl=notice_display&id=9719 Analyse du chaos dans un système d’équations différentielles fractionnaires [texte imprimé] / Tarek Houmor, Auteur ; N. Hamri, Directeur de thèse . - constantine [Algérie] : Université Constantine 1, 2014 . - 136 f. ; 30 cm.
2 copies imprimées disponibles
Langues : Français (fre)
Catégories : Français - Anglais
MathématiquesTags : Dérivées d’ordre fractionnaire Chaos Exposants de Lyapounov Fer à cheval
topologique Test 0-1 Synchronisation du chaos Fractional-order derivatives Lyapounov exponent Topological horseshoe 0-1 test Chaos synchronization مشتقات ذات رتبة كسرية الفوضى قوى ليابونوف الحدوة الطوبولوجية الإختبار
1-0 التزامنIndex. décimale : 510 Mathématiques Résumé : In this thesis, we focus on the differential equations of fractional order systems exhibiting chaotic dynamics. Particular attention has been paid to a nonlinear system of fractional differential equations modeling the phenomenon of nuclear magnetic resonance : the Bloch system. A qualitative analysis of the dynamics of this system has been made, including some basic properties : bifurcations, periodic windows and routes to chaos. These properties were analyzed numerically by bifurcation diagram, phase portraits and Lyapunov exponents .
The chaotic behavior of this system was confirmed by the existence of a positive Lyapunov exponent.
On the other hand, the topological horseshoe was found, rigorously proving the chaotic nature of our system for certain parameter values, this method is considered as an excellent substitute for the Lyapunov spectrum method, less reliable numerically.
0-1 test provides a simple and efficient criterion for the distinction chaotic solutions of regular
orbits, we have successfully applied this test in our work.
Finally, the method of non-linear control was extended to realize the identical synchronization of two fractional Bloch systems. The results were proven analytically using stability conditions for fractional systems. A numerical simulation was performed to validate the results.Diplôme : Doctorat en sciences En ligne : ../theses/math/HOU6606.pdf Format de la ressource électronique : Permalink : https://bu.umc.edu.dz/md/index.php?lvl=notice_display&id=9719 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité HOU/6606 HOU/6606 Thèse Bibliothèque principale Thèses Disponible Documents numériques
texte intégreAdobe Acrobat PDF
