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1 | 1 | # [Plotting Nullclines and Steady States in Phase Space](@id nullcline_plotting)
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2 |
| -In this tutorial we will show how to extract a system's steady states and [nullclines](https://en.wikipedia.org/wiki/Nullcline), and how to plot these in [phase space](https://en.wikipedia.org/wiki/Phase_space). Generally, while nullclines are not directly needed for much analysis, plotting these can give some understanding of a system's steady state and stability properties. |
| 2 | +In this tutorial we will show how to extract a system's steady states and [nullclines](https://en.wikipedia.org/wiki/Nullcline), and how to plot these in [phase space](https://en.wikipedia.org/wiki/Phase_space). Generally, while nullclines are not directly needed for most types analysis, plotting these can give some understanding of a system's steady state and stability properties. |
3 | 3 |
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4 | 4 | For an ordinary differential equation
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5 | 5 | ```math
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@@ -32,10 +32,10 @@ sss = hc_steady_states(bs_switch, ps; show_progress = false)
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32 | 32 |
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33 | 33 | Finally, we will compute the nullclines. First we create a function which, for species values $(X,Y)$, returns the evaluation of the model's ODE's right-hand side.
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34 | 34 | ```@example nullcline_plotting
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35 |
| -nlprob = NonlinearProblem(complete(nlsys), [X => 0.0, Y => 0.0], ps) |
| 35 | +nlprob = NonlinearProblem(bs_switch, [X => 0.0, Y => 0.0], ps) |
36 | 36 | function get_XY(Xval, Yval)
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37 | 37 | prob = Catalyst.remake(nlprob; u0 = [X => Xval, Y => Yval])
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38 |
| - return prob[equations(nlsys)[2].rhs], prob[equations(nlsys)[1].rhs] |
| 38 | + return nlprob.f(prob.u0, prob.p) |
39 | 39 | end
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40 | 40 | ```
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41 | 41 | Next, we plot our nullclines by using Plot.jl's [`contour` function](https://docs.juliaplots.org/latest/series_types/contour/). Here, we plot the $0$ contour lines (which corresponds to the nullclines) for both the $X$ and $Y$ nullclines. We will plot the steady states using `scatter`. We use the `steady_state_stability` function to [compute steady state stabilities](@ref steady_state_stability) (and use this to determine how to plot the steady state markers).
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