Résumé:
The aimofthisthesisistostudythedynamicsofaTuring-typereaction-di usion
model,i.e.studyareaction-di usionmodelthatexhibitsTuringproperties,whereas
the reaction-di usionde nesthemechanisminwhichseveralinteractingchemicalsor
agentsreacttogetherwhiledi usingorspreadingacrossaliquidorgaseousmedium
simultaneously,usually,theseprocessesarestudiedfortheirabilitytoproducenontrivial
patterns thatevolveovertime.Suchpatternsaredrivenbydi usion,alsoreferredtoas
TuringstructuresorTuringpatterns.TheTuringpatternsaremeasuredinthepresenceof
di usion, butarenotpresentintheabsenceofdi usion,thismechanismecalled"di usion-
driveninstability"or"Turinginstability".Inthiswork,thestudywasrelated"thewell-
knownDegn-Harrisonreactiondi usionmodelanditsgeneralization".Ourthechniqueto
provetheasymptoticstabilityofthesteadystatesolutionisbasedontheeigen-analysis,
the Poincar e{BendixsontheoremandthedirectLyapunovmethod.
