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TorkelEisaacsas
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Update docs/src/steady_state_functionality/examples/nullcline_plotting.md
Co-authored-by: Sam Isaacson <[email protected]>
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docs/src/steady_state_functionality/examples/nullcline_plotting.md

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@@ -10,16 +10,7 @@ For an ordinary differential equation
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\frac{dx_n}{dt} &= f_n(x_1, x_2, ..., x_n) \\
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\end{aligned}
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```
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the nullclines are the curves
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```math
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\begin{aligned}
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0 &= f_1(x_1, x_2, ..., x_n) \\
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0 &= f_2(x_1, x_2, ..., x_n) \\
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&\vdots\\
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0 &= f_n(x_1, x_2, ..., x_n) \\
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\end{aligned}
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```
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where the $i$'th nullclines is the curve along which $\frac{dx_i}{dt} = 0$. Generally, nullclines are primarily computed for models with 2 variables (as these can be easily plotted).
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the $i$'th nullcline is the surface along which $\frac{dx_i}{dt} = 0$, i.e. the implicit surface given by $f_i(x_1,\dots,x_n) = 0$. Nullclines are frequently used when visualizing the phase-planes of two-dimensional models (as these can be easily plotted).
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## [Computing nullclines and steady states for a bistable switch](@id nullcline_plotting_computation)
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For our example we will use a simple bistable switch model, consisting of two species ($X$ and $Y$) which mutually inhibit each other through repressive Hill functions. We will create our model [programmatically](@ref programmatic_CRN_construction).

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