113 citations · 176 across the 22 of their papers we have counts for
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Explicit Second-Order Bounds on the Domain of Validity for Lyapunov-Schmidt Reduction
Pranav Gupta, Ravi Banavar, Anastasia Bizyaeva
Lyapunov-Schmidt reduction is a widely used dimensionality reduction technique for bifurcation analysis in high-dimensional systems. While classical formulations guarantee the loca…
Behavior of Nonlinear Opinion Dynamics over Large Networks
Yu Xing, Anastasia Bizyaeva, Karl H. Johansson
Opinion dynamics have been studied for decades across disciplines, with much of the theoretical literature focusing on behaviors such as consensus, polarization, and clustering. Al…
Bounds of Validity for Bifurcations of Equilibria in a Class of Networked Dynamical Systems
Pranav Gupta, Ravi Banavar, Anastasia Bizyaeva
Local bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dyna…
Bifurcation analysis of an opinion dynamics model coupled with an environmental dynamics
Anthony Couthures, Anastasia Bizyaeva, Vineeth S. Varma +2
We consider an opinion dynamics model coupled with an environmental dynamics. Based on a forward invariance argument, we can simplify the analysis of the asymptotic behavior to the…
Learning Communities from Equilibria of Nonlinear Opinion Dynamics
Yu Xing, Anastasia Bizyaeva, Karl H. Johansson
This paper studies community detection for a nonlinear opinion dynamics model from its equilibria. It is assumed that the underlying network is generated from a stochastic block mo…
Adaptive bias for dissensus in nonlinear opinion dynamics with application to evolutionary division of labor games
Tyler M. Paine, Anastasia Bizyaeva, Michael R. Benjamin
This paper addresses the problem of adaptively controlling the bias parameter in nonlinear opinion dynamics (NOD) to allocate agents into groups of arbitrary sizes for the purpose…
Estimates on the domain of validity for Lyapunov-Schmidt reduction
Pranav Gupta, Anastasia Bizyaeva, Ravi Banavar
Lyapunov-Schmidt reduction is a dimensionality reduction technique in nonlinear systems analysis that is commonly utilised in the study of bifurcation problems in high-dimensional…