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math.DS2024
Global Dynamics of Ordinary Differential Equations: Wall Labelings, Conley Complexes, and Ramp Systems
Marcio Gameiro, Tomáš Gedeon, Hiroshi Kokubu +5
We introduce a combinatorial topological framework for characterizing the global dynamics of ordinary differential equations (ODEs). The approach is motivated by the study of gene…
math.DS2021
Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities
William Duncan, Tomas Gedeon, Hiroshi Kokubu +2
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge…