Analytical Results

From the linear analysis one can find that the critical curve is given by:

Options[Plot]

We call two packages

Needs["Graphics`FilledPlot`"]
Needs["Graphics`InequalityGraphics`"]

We define text and text properties

t = "Times";
opty[n_] := Sequence[FontFamily->t, FontWeight->"Bold",FontSize->n, FontColor->RGBColor[1,1,0]]
optb[n_] := Sequence[FontFamily->t, FontWeight->"Bold",FontSize->n, FontColor->RGBColor[0,0,0]]

Using the Block command, we plot

Block[{$DisplayFunction=Identity},
p1 = FilledPlot[{mk[x],1},{x,0,10},PlotRange->{0,5},FrameLabel->{"go","k"},Frame->True,RotateLabel->False,Fills->{RGBColor[1,0,0],RGBColor[1,0,0]}];
p2 = InequalityPlot[{ck[x]<y<5},{x,1,10},{y,0,5},PlotRange->{0,5},FrameLabel->{"go","k"},Frame->True,RotateLabel->False,Fills->{RGBColor[0,0,1]}];
    ]

figMLVM = Show[{p1,p2,Graphics[Line[{{1,0},{1,5}}]]},PlotRange->{{0,10},{0,5}},Epilog->{
Text[StyleForm["Oscillations",opty[14]],{4,4}],
Text[StyleForm["Unphysical     g < 0",opty[14]],{4,0.5}],
Text[StyleForm["r< 0",opty[14]],{0.1,1.5},{-1,-1}],
Text[StyleForm["SS",optb[14]],{1.,3}]}];

Any point in the red region represent a totally unphysical situation in the world of negative concentrations.   But any point in the blue region yields oscillations. Any pointin the white region and  between the  line and red region yields ONLY stable steady states

Block[{$DisplayFunction=Identity},
p1 = FilledPlot[{mgo[x]},{x,1,5},PlotRange->{0,5},FrameLabel->{"k","go"},Frame->True,RotateLabel->False,
Fills->{RGBColor[1,0,0],RGBColor[1,0,0]}];
p1b = FilledPlot[{10},{x,0,1},PlotRange->{0,5},FrameLabel->{"k","go"},Frame->True,RotateLabel->False,
Fills->{RGBColor[1,0,0],RGBColor[1,0,0]}];
p2 = InequalityPlot[{cgo[x]<y<10},{x,1,5},{y,0,10},PlotRange->{0,5},FrameLabel->{"k","go"},Frame->True,RotateLabel->False,Fills->{RGBColor[0,0,1]}];
]

figMLVM2 = Show[{p1,p1b,p2,Graphics[Line[{{0,1},{5,1}}]],Graphics[Line[{{1,0},{1,10}}]]},PlotRange->{{0,5},{0,10}},Epilog->{
Text[StyleForm["Oscillations",opty[14]],{4,4}],
Text[StyleForm["r < 0",opty[14]],{1.5,0.5}],
Text[StyleForm["g< 0",opty[14]],{0.1,1.5},{-1,-1}],
Text[StyleForm["SS",optb[14]],{2.,1.5}]}];

Any point in the red region represent a totally unphysical situation in the world of negative concentrations.  Any pointin the white region and  between the  line and red region yields ONLY stable steady states

Created by Mathematica  (September 7, 2006)