Dynamics of the Lengyel-Epstein Reaction-Diffusion System and its Generalizations
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Date
2021
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Djamel Mansouri
Abstract
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.