12 citations · 32 across the 5 of their papers we have counts for
6 papers · 1 filter
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…
The Morse equation in the Conley index theory for discrete multivalued dynamical systems
Bogdan Batko
A recent generalization of the Conley index to discrete multivalued dynamical systems without a continuous selector is motivated by applications to data-driven dynamics. In the pre…
Conley index approach to sampled dynamics
Bogdan Batko, Konstantin Mischaikow, Marian Mrozek +1
The topological method for the reconstruction of dynamics from time series [K. Mischaikow, M. Mrozek, J. Reiss, A. Szymczak. Construction of Symbolic Dynamics from Experimental Tim…
Linking combinatorial and classical dynamics: Conley index and Morse decompositions
Bogdan Batko, Tomasz Kaczynski, Marian Mrozek +1
We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system F…
Weak index pairs and the Conley index for discrete multivalued dynamical systems. Part II: properties of the index
Bogdan Batko
Motivation to revisit the Conley index theory for discrete multivalued dynamical systems stems from the needs of broader real applications, in particular in sampled dynamics or in…
Weak index pairs and the Conley index for discrete multivalued dynamical systems
Bogdan Batko, Marian Mrozek
Motivated by the problem of reconstructing dynamics from samples we revisit the Conley index theory for discrete multivalued dynamical systems. We introduce a new, less restrictive…