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- James P Bagrow, Erik M Bollt
- Physical review. E, Statistical, nonlinear, and…
- 2005

We propose a method of community detection that is computationally inexpensive and possesses physical significance to a member of a social network. This method is unlike many divisive and agglomerative techniques and is local in the sense that a community can be detected within a network without requiring knowledge of the entire network. A global… (More)

- Daniel J. Stilwell, Erik M. Bollt, D. Gray Roberson
- SIAM J. Applied Dynamical Systems
- 2006

In previous work [J. D. Skufca and E. Bollt, Mathematical Biosciences and Engineering, 1 (2004), pp. 347–359], empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of… (More)

We propose a novel method of community detection that is computationally inexpensive and possesses physical significance to a member of a social network. This method is unlike many divisive and agglomerative techniques and is local in the sense that a community can be detected within a network without requiring knowledge of the entire network. A global… (More)

- Maurizio Porfiri, Daniel J. Stilwell, Erik M. Bollt
- IEEE Trans. on Circuits and Systems
- 2008

We assess synchronization of oscillators that are coupled via a time-varying stochastic network, modeled as a weighted directed random graph that switches at a given rate between a set of possible graphs. The existence of any graph edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted… (More)

- Joseph D Skufca, Erik M Bollt
- Mathematical biosciences and engineering : MBE
- 2004

We consider systems that are well modelled as networks that evolve in time, which we call Moving Neighborhood Networks. These models are relevant in studying cooperative behavior of swarms and other phenomena where emergent interactions arise from ad hoc networks. In a natural way, the time-averaged degree distribution gives rise to a scale-free network.… (More)

- J. Suna, E. M. Bollt
- 2009

We derive a master stability function (MSF) for synchronization in networks of coupled dynamical systems with small but arbitrary parametric variations. Analogous to the MSF for identical systems, our generalized MSF simultaneously solves the linear-stability problem for near-synchronous states (NSS) for all possible connectivity structures. We also derive… (More)

Erik M. Bollt,1 Theodore Stanford,2 Ying-Cheng Lai,3 Karol Życzkowski4,5 1Mathematics Department, 572 Holloway Road, U.S. Naval Academy, Annapolis, Maryland 21402-5002 2Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001 3Departments of Mathematics, Electrical Engineering, and Physics, Center for Systems… (More)

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows for rigorous statistical comparison between networks. Dynamic processes such as percolation can be visualized using… (More)

An increasingly popular method of encoding chaotic time-series from physical experiments is the so-called threshold crossings technique, where one simply replaces the real valued data with symbolic data of relative positions to an arbitrary partition at discrete times. The implication has been that this symbolic encoding describes the original dynamical… (More)

- Jie Sun, Erik M. Bollt
- 2013

Inference of causality is central in nonlinear time series analysis and science in general. A popular approach to infer causality between two processes is to measure the information flow between them in terms of transfer entropy. Using dynamics of coupled oscillator networks, we show that although transfer entropy can successfully detect information flow in… (More)