9 citations · 9 across the 3 of their papers we have counts for
3 papers
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…
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…
Global Dynamics for Steep Sigmoidal Nonlinearities in Two Dimensions
Tomas Gedeon, Shaun Harker, Hiroshi Kokubu +2
We introduce a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. Motivated by models of regulatory networks, we…