Stability and Bifurcations and Control in Fractional Order Chaotic Systems

Chettouh, Besma (2024) Stability and Bifurcations and Control in Fractional Order Chaotic Systems. Doctoral thesis, Université Mohamed Khider (Biskra - Algérie).

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Abstract

The inclusion of fractional-order dynamics in the study of nonlinear systems has broadened our understanding of complex behaviors, such as stability, chaos and bifurcations, and has opened up new possibilities in control theory. These systems involve derivatives and integrals of non-integer order, introducing a new level of flexibility and versatility in modeling realworld phenomena. This thesis aims to study the stability and bifurcations in a fractional order chaotic systems and the control of chaos. To achieve our goal we introduced in the first tow chapters the necessary basic notions such as: fractional derivation, chaos theory, stability of fractional systems and bifurcation theory. The main results of this thesis are presented in the last tow chapters where we gave the necessary and su¢ cient conditions for stability, we showed the existence of Hopf bifurcations in both cases: integer and fractional also we proved the effect of fractional order in the critical point location of Hopf’s bifurcation points, stability and chaos control.

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