Templator

The minimal Templator was analyzed first by Peacock-Lopez (Peacock-Lopez, E., Radov, D. B., Flesner, C.S., Biophys. Chem. 1997, 65, 171-178).  The minimal Templator is given by the following differential equations:

odes = {x^′[t] == ro - x[t]^2 y[t], y^′[t] == x[t]^2 y[t] - y[t]/(K + y[t]), x[0] == xi, y[0] == yi}

{x^′[t] == ro - x[t]^2 y[t], y^′[t] == x[t]^2 y[t] - y[t]/(K + y[t]), x[0] == xi, y[0] == yi}

Typical values will give stable oscillations

par = {ro→0.3, K→0.3, xi->5., yi->15.}

{ro→0.3, K→0.3, xi→5., yi→15.}

The numerical integration of the ODE's is accomplished by NDSolve

solmin = NDSolve[odes/.par, {x, y}, {t, 0, 100}]

{{x→InterpolatingFunction[{{0., 100.}}, <>], y→InterpolatingFunction[{{0., 100.}}, <>]}}

To plot the integrated ODEs, we use a substitution, /., within the Plot command

fig1 = Plot[Evaluate[{x[t], y[t]}/.solmin], {t, 0, 100}, PlotStyle→ {{Dashing[{0.02}], Hue[1.], Thickness[0.01]}, {Thickness[0.01]}}, Frame→True] ;

[Graphics:../HTMLFiles/MATH5_TUT1_827.gif]

fig2 = ParametricPlot[Evaluate[{x[t],y[t]}/.solmin],{t,0,100}, PlotStyle→{{Dashing[{0.02}],Thickness[0.01],Hue[.8]}},Frame->True];

[Graphics:../HTMLFiles/MATH5_TUT1_828.gif]

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