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Exothermic reaction stationary solutions放热反应固定解决方案.ppt

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ponentreaction-ovingcoordinate:Integrate:StatewithlowerpotentialadvancesMaxwellconstruction:a=0PhaseplanePhaseplaneu–putationofapropagatingfrontIntegrate:Ifintegrationproceedstou2,increasecIfpdropsto0andintegrationstops,arrowtheintegraluntilp(u2–d)iscloseto0DependenceofthepropagationvelocityontheparameteraUnstablepropagatingwavetrainsIntegrate:withinitialconditionp(uc)=0whereu1<uc<u0;rajectoriesofwavetrainsfora==-diffusionsystemu–activatorShort-rangeifd<<1v–inhibitorasimpleexample:cubic(fast)&linear(slow)(FitzHugh–Nagumo)ponentsystem:stabilityStabilityboundaryLinearizationStationarysolutionJacobian(positive)Det(L)minimalatMustbe:fu+gv<0,fu+d2gv<0rapidlydiffusinginhibitorAssume:fu>0(activator),gv<0(inhibitor)BrusselatormodelHopfinstability:b=1+a2,k=0Linearization:Stationarysolutionus=a,vs=b/aJacobianDetminimalatAB,2A+B3A+flowofATuringinstability:TuringprecedesHopfifd<1–1/aDet=ponentfast–slowsystemu–activatorFastife<<1v–inhibitor(a)relaxationoscillations(b)bistable(c)ponentsystemwithseparatedscalessynclinaldisposition;thedynamicalsystemisbistable,stationaryfrontisunstable,nostationaryinhomogeneousstatesanticlinaldisposition,thedynamicalsystemisoscillatory;nostationaryhomogeneousstates,,thedynamicalsystemisbistableexcitable,

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