Traditional linear stability analysis based on matrix diagonalization is a
computationally intensive O(n3) process for n-dimensional systems of
differential equations, posing substantial limitations for the exploration of
Turing systems of pattern formation where an additional wave-number parameter
needs to be investigated. In this study, we introduce an efficient O(n)
technique that leverages Gershgorin's theorem to determine upper limits on
regions of parameter space and the wave number beyond which Turing
instabilities cannot occur. This method offers a streamlined avenue for
exploring the phase diagrams of other complex multiparametric models, such as
those found in systems biology