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docs/src/steady_state_functionality/steady_state_stability_computation.md

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Catalyst currently computes steady state stabilities using the naive approach of checking whether a system's largest eigenvalue real part is negative. While more advanced stability computation methods exist (and would be a welcome addition to Catalyst), there is no direct plans to implement these. Furthermore, Catalyst uses a tolerance `tol = 10*sqrt(eps())` to determine whether a computed eigenvalue is far away enough from 0 to be reliably used. This threshold can be changed through the `tol` keyword argument.
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## Basic examples
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## [Basic examples](@id steady_state_stability_basics)
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Let us consider the following basic example:
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```@example stability_1
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using Catalyst
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```
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## Pre-computing the Jacobian to increase performance when computing stability for many steady states
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## [Pre-computing the Jacobian to increase performance when computing stability for many steady states](@id steady_state_stability_jacobian)
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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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In this example we use the self-activation loop from previously, pre-computes its Jacobian, and uses it to multiple `steady_state_stability` calls:

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