From a5aeaf88ab660fc719cf95a883edfb56db14d47b Mon Sep 17 00:00:00 2001 From: Sam Isaacson Date: Tue, 23 Jul 2024 10:12:39 -0400 Subject: [PATCH] Update steady_state_stability_computation.md --- .../steady_state_stability_computation.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/src/steady_state_functionality/steady_state_stability_computation.md b/docs/src/steady_state_functionality/steady_state_stability_computation.md index c51b55cd2a..8404498231 100644 --- a/docs/src/steady_state_functionality/steady_state_stability_computation.md +++ b/docs/src/steady_state_functionality/steady_state_stability_computation.md @@ -2,7 +2,7 @@ After system steady states have been found using [HomotopyContinuation.jl](@ref homotopy_continuation), [NonlinearSolve.jl](@ref steady_state_solving), or other means, their stability can be computed using Catalyst's `steady_state_stability` function. Systems with conservation laws will automatically have these removed, permitting stability computation on systems with singular Jacobian. !!! warning - 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. + Catalyst currently computes steady state stabilities using the naive approach of checking whether a system's largest eigenvalue real part is negative. Furthermore, Catalyst uses a tolerance `tol = 10*sqrt(eps())` to determine whether a computed eigenvalue is far away enough from 0 to be reliably considered non-zero. This threshold can be changed through the `tol` keyword argument. ## [Basic examples](@id steady_state_stability_basics) Let us consider the following basic example: @@ -60,4 +60,4 @@ nothing # hide ``` !!! warning - 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. \ No newline at end of file + 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.