MUDEL JÄNESTE JA REBASTE NÄITEL

<<Graphics`Arrow`

α = 1.4;  
β = 0.02; 
γ = 0.1; 
δ = 0.001; 
sol = NDSolve[
{x'[t] == α x[t] - β x[t] y[t],
 y'[t] == - γ y[t] + δ x[t] y[t],
 x[0] == 100, y[0] == 40 }, {y, x}, {t, 0, 80} ];

 Plot[Evaluate[{x[t], y[t]} /. sol], {t, 0, 80}, 
   PlotStyle -> {RGBColor[1,0,0], RGBColor[0,0,1]},
   PlotRange->All, AxesStyle -> Arrowheads[{0.025}]]

gr1 = ParametricPlot[Evaluate[{x[t], y[t]} /. sol], {t, 0, 20}, 
AxesStyle -> Arrowheads[{0.025}], 
	Epilog -> {PointSize[0.01],Point[{γ/δ, α/β}],
	Dashing[{0.02,0.02}], Line[{{γ/δ, 0},{γ/δ, 110}}],
	Line[{{0, α/β},{420, α/β}}]
	}]

TableForm[Table[{t,(x/.sol[[1]])[t],(y/.sol[[1]])[t]},{t,0,30}],
TableHeadings->{None,{"t", "x[t]", "y[t]"}}]

Remove["Global`*"]

<<Graphics`ImplicitPlot`

<<Graphics`Arrow`

Faasidiagrammid :

α=1.4; 
β=0.02; 
γ=0.1;
δ=0.001;

KMax=((((α/(β E))))^α)((((γ/(δ E))))^γ)

Faasidiagrammid=Show[Flatten[Table[ImplicitPlot[{u==((y^α)/(E^(β y)))((x^γ)/(E^( δ x))),x==(γ/δ),y==(α/β)}, {x,0,550},{y,0,140}, AspectRatio->1,PlotPoints->50,AxesStyle->Arrowheads[{0.025}],PlotStyle->{{RGBColor[0,0,0.5],AbsoluteThickness[0.7]},{Hue[0], AbsoluteDashing[{4}],AbsoluteThickness[0.5]},{Hue[0], AbsoluteDashing[{4}],AbsoluteThickness[0.5]}}],{u,Floor[KMax],100,-4}]]]

Faasidiagrammid teiste parameetritega :

Algparameetrid :

α:=1.3; β:=0.03; γ:=0.1;δ:=0.0015;

KMax=((((α/(β E))))^α)((((γ/(δ E))))^γ)

Faasidiagrammid=Show[Flatten[Table[ImplicitPlot[{u==((y^α)/(E^(β y)))((x^γ)/(E^( δ x))),x==(γ/δ),y==(α/β)}, {x,0,650},{y,0,110}, AspectRatio->1,PlotPoints->50,AxesStyle->Arrowheads[{0.025}],PlotStyle->{{RGBColor[0,0,0.5],AbsoluteThickness[1]},{Hue[0], AbsoluteDashing[{4}],AbsoluteThickness[0.6]},{Hue[0], AbsoluteDashing[{4}],AbsoluteThickness[0.6]}}],{u,Floor[KMax],27,-1}]]]

Ebasoodsad tingimused jäneste jaos

α = 0.7;  
β = 0.1; 
γ = 0.1; 
δ = 0.001; 
sol = NDSolve[
{x'[t] == α x[t] - β x[t] y[t],
 y'[t] == - γ y[t] + δ x[t] y[t],
 x[0] == 100, y[0] == 40 }, {y, x}, {t, 0, 2} ];

 Plot[Evaluate[{x[t], y[t]} /. sol], {t, 0, 2}, 
   PlotStyle -> {{RGBColor[1,0,0],AbsoluteThickness[1]},
   {AbsoluteThickness[0.8], RGBColor[0,0,1]}},
   AxesStyle -> Arrowheads[{0.03}],
   PlotRange->All]

TableForm[Table[{t,(x/.sol[[1]])[t],(y/.sol[[1]])[t]},{t,0,2,0.1}],
TableHeadings->{None,{"t", "x[t]", "y[t]"}}]

α = 0.7;  
β = 0.1; 
γ = 0.1; 
δ = 0.001; 
sol = NDSolve[
{x'[t] == α x[t] - β x[t] y[t],
 y'[t] == - γ y[t] + δ x[t] y[t],
 x[0] == 100, y[0] == 40 }, {y, x}, {t, 0, 65} ];

TableForm[Table[{t,(x/.sol[[1]])[t],(y/.sol[[1]])[t]},{t,0,65,1}],
TableHeadings->{None,{"t", "x[t]", "y[t]"}}]

Remove["Global`*"]

<<Graphics`ImplicitPlot`

<<Graphics`Arrow`

faasidiagramm

α=0.7; 
β=0.1; 
γ=0.1;
δ=0.001;

KMax=((((α/(β E))))^α)((((γ/(δ E))))^γ)

x=100;
y=40;

u==((y^α)/(E^(β y)))((x^γ)/(E^( δ x)))

x=.;
y=.;

ImplicitPlot[{0.347404==((y^α)/(E^(β y)))((x^γ)/(E^( δ x))),x==(γ/δ),y==(α/β)}, {x,0,2570},{y,0,40},AspectRatio->0.63, PlotPoints->50,AxesStyle->Arrowheads[{0.025}],PlotStyle->{{RGBColor[0,0,0.55],AbsoluteThickness[1]},{Hue[0], AbsoluteDashing[{4}],AbsoluteThickness[0.5]},{Hue[0], AbsoluteDashing[{4}],AbsoluteThickness[0.5]}}]