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arXiv · 2309.04741

Upper limits on the robustness of Turing models and other multiparametric dynamical systems

Roozbeh H. Pazuki·Robert G. Endres
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Abstract

Traditional linear stability analysis based on matrix diagonalization is a computationally intensive $O(n^3)$ 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.

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Roozbeh H. Pazuki, Robert G. Endres. 2023-09-09. Upper limits on the robustness of Turing models and other multiparametric dynamical systems. https://arxiv.org/abs/2309.04741

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