Browsing by Author "Djamel Mansouri"

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    Dynamics of the Lengyel-Epstein Reaction-Diffusion System and its Generalizations
    (Djamel Mansouri, 2021) Djamel Mansouri
    The aim of this thesis is to study some generalizations of Lengyel-Epstein Reaction-Diffusion System . Where we proposed and studied the dynamics of a fractional system consistent with the Lengyel - Epstein model, we established sufficient conditions for the stability of the local convergence of the unique equilibrium of the system by the linearization method, we used Lyapunov’s direct method to establish the global asymptotic stability of the steady state solution. . Moreover, we studied the stability and instability of the generalized Lengyel - Epstein system as well as examining the Hopf-bifurcation of the system in diffusion-free and diffusive states. The numerical results obtained using the finite difference method were presented to confirm and verify theoretical results.