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Update docs/src/catalyst_applications/bifurcation_diagrams.md
Co-authored-by: Sam Isaacson <[email protected]>
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docs/src/catalyst_applications/bifurcation_diagrams.md

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@@ -88,7 +88,7 @@ Here, in the bistable region, we only see a single branch. The reason is that th
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## Systems with conservation laws
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Some systems are under-determined determined at steady-state, so that for a given parameter set they have an infinite number of possible steady state solutions, preventing bifurcation diagrams from being computed. Similar to when we [compute steady states for fixed parameter values](@ref homotopy_continuation_conservation_laws), we can utilise Catalyst's ability to detect and eliminate conservation laws to resolve this issue. This requires us to provide information of the species concentrations at which we wish to compute the bifurcation diagram (to determine the values of conserved quantities). These are provided to the `BifurcationProblem` using the `u0` argument.
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To illustrate this, we will create a simple model of a kinase that is produced and degraded (at rates *p* and *d*). The kinase facilitates the phosphorylation of a protein (*X*), which is dephosphorylated at a constant rate. For this system, we will compute a bifurcation diagram, showing how the concentration of the phosphorylated protein (*Xp*) depends on the degradation rate of the kinase (*d*). We will set the total amount of protein (*X+Xp*) to *1.0*.
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To illustrate this, we will create a simple model of a kinase that is produced and degraded (at rates $p$ and $d$). The kinase facilitates the phosphorylation of a protein ($X$), which is dephosphorylated at a constant rate. For this system, we will compute a bifurcation diagram, showing how the concentration of the phosphorylated protein ($Xp$) depends on the degradation rate of the kinase ($d$). We will set the total amount of protein ($X+Xp$) to $1.0$.
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```@example ex2
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using BifurcationKit, Catalyst, Plots
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kinase_model = @reaction_network begin

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