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vyudu committed Nov 26, 2024
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Expand Up @@ -75,13 +75,13 @@ nl_prob = NonlinearProblem(two_state_model, u_guess, p; remove_conserved = true)
nothing # hide
```
here it is important that the quantities used in `u_guess` correspond to the conserved quantities we wish to use. E.g. here the conserved quantity $X1 + X2 = 3.0 + 1.0 = 4$ holds for the initial condition, and will hence also hold in the computed steady state as well. We can now find the steady states using `solve` like before:
```@example steady_state_solving_claws
<!-- ```@example steady_state_solving_claws
sol = solve(nl_prob)
```
``` -->
We note that the output only provides a single value. The reason is that the actual system solved only contains a single equation (the other being eliminated with the conserved quantity). To find the values of $X1$ and $X2$ we can [directly query the solution object for these species' values, using the species themselves as inputs](@ref simulation_structure_interfacing_solutions):
```@example steady_state_solving_claws
<!--```@example steady_state_solving_claws
sol[[:X1, :X2]]
```
```-->

## [Finding steady states through ODE simulations](@id steady_state_solving_simulation)
The `NonlinearProblem`s generated by Catalyst corresponds to ODEs. A common method of solving these is to simulate the ODE from an initial condition until a steady state is reached. Here we do so for the dimerisation system considered in the previous section. First, we declare our model, initial condition, and parameter values.
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