5 citations · 10 across the 5 of their papers we have counts for
5 papers
Symmetry Analysis of Coupled Scalar Systems under Time Delay
Fatihcan M. Atay, Haibo Ruan
We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extr…
Classification of Codimension-1 Singular Bifurcations in Low-dimensional DAEs
Ivan Ovsyannikov, Haibo Ruan
The study of bifurcations of differential-algebraic equations (DAEs) is the topic of interest for many applied sciences, such as electrical engineering, robotics, etc. While some o…
Synchrony in Gene Regulatory Networks
Manuela Aguiar, Ana Dias, Haibo Ruan
We consider two mathematical dynamical models of gene regulatory networks (GRNs) and obtain results on robust synchronization on these dynamical models based on the existing theore…
Reduced Lattices of Synchrony Subspaces and their Indices
Hiroko Kamei, Haibo Ruan
For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces that are invariant under the network adjacency matrix. The complete lattice of synchrony subs…
Degeneracy Index and Poincaré-Hopf Theorem
Haibo Ruan, Jorge Zanelli
A degenerate dynamical system is characterized by a state-dependent multiplier of the time derivative of the state in the time evolution equation. It can give rise to Hamiltonian s…