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docs/src/catalyst_applications/steady_state_stability_computation.md

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@@ -33,6 +33,9 @@ Next, we can apply `steady_state_stability` directly to this steady state vector
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steady_state_stability(steady_states, sa_loop, ps)
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```
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!!! note
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For systems with [conservation laws](@ref homotopy_continuation_conservation_laws), `steady_state_jac` must be supplied a `u0` vector (indicating species concentrations for conservation law computation). This is required to eliminate the conserved quantities, preventing a singular Jacobian. These are supplied using the `u0` optional argument.
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## Pre-computing the Jacobian to increase performance when computing stability for many steady states
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Catalyst uses the system Jacobian to compute steady state stability, and the Jacobian is computed once for each call to `steady_state_stability`. If you repeatedly compute stability for steady states of the same system, pre-computing the Jacobian and supplying it to the `steady_state_stability` function can improve performance.
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@@ -48,7 +51,4 @@ ps_2 = [:v => 4.0, :K => 1.5, :n => 2, :d => 1.0]
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steady_states_2 = hc_steady_states(sa_loop, ps)
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stability_2 = steady_state_stability(steady_states_2, sa_loop, ps_2; ss_jac=ss_jac)
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nothing # hide
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```
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!!! note
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For systems with [conservation laws](@ref homotopy_continuation_conservation_laws), `steady_state_jac` must be supplied a `u0` vector (indicating species concentrations for conservation law computation). This is required to eliminate the conserved quantities, preventing a singular Jacobian. These are supplied using the `u0` optional argument.
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```

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