155 citations · 542 across the 36 of their papers we have counts for
45 papers
Computing the Conley Index: a Cautionary Tale
Konstantin Mischaikow, Charles Weibel
This paper concerns the computation and identification of the (homological) Conley index over the integers, in the context of discrete dynamical systems generated by continuous map…
Data-Efficient Characterization of the Global Dynamics of Robot Controllers with Confidence Guarantees
Ewerton R. Vieira, Aravind Sivaramakrishnan, Yao Song +5
This paper proposes an integration of surrogate modeling and topology to significantly reduce the amount of data required to describe the underlying global dynamics of robot contro…
Conditioned Weiner Processes as Nonlinearities: A Rigorous Probabilistic Analysis of Dynamics
Konstantin Mischaikow, Cameron Thieme
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topolog…
Identifying Nonlinear Dynamics with High Confidence from Sparse Data
Bogdan Batko, Marcio Gameiro, Ying Hung +3
We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic b…
Global analysis of regulatory network dynamics: equilibria and saddle-node bifurcations
Shane Kepley, Konstantin Mischaikow, Elena Queirolo
In this paper we describe a combined combinatorial/numerical approach to studying equilibria and bifurcations in network models arising in Systems Biology. ODE models of the dynami…
Morse Graphs: Topological Tools for Analyzing the Global Dynamics of Robot Controllers
Ewerton R. Vieira, Edgar Granados, Aravind Sivaramakrishnan +3
Understanding the global dynamics of a robot controller, such as identifying attractors and their regions of attraction (RoA), is important for safe deployment and synthesizing mor…