Abbad, Abir2022-03-292022-03-292021http//localhost:8080/jspui/handle/123456789/2429The 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.enReaction-Di usion Systems ,TuringInstability , GlobalExistence , LyapunovFunc- tional , StabilityAnalysisThesis