9 citations · 20 across the 6 of their papers we have counts for
6 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…
Topological computation analysis of meteorological time-series data
Hidetoshi Morita, Masaru Inatsu, Hiroshi Kokubu
A topological computation method, called the MGSTD method, is applied to time-series data obtained from meteorological measurement. The method gives decomposition of the dynamics i…
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…
Inducing a map on homology from a correspondence
Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow +1
We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codoma…
Formation Mechanism of a Basin of Attraction for Passive Dynamic Walking Induced by Intrinsic Hyperbolicity
Ippei Obayashi, Shinya Aoi, Kazuo Tsuchiya +1
Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and th…