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We show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function, which can be tailored to one’s choice of stability requirement. This solves, once and for all, the problem of synchronous stability for any… (More)

- Mauricio Barahona, Louis M Pecora
- Physical review letters
- 2002

We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shortcuts… (More)

-Although the motions of independent chaotic systems are uncorrelated with each other, it is possible under some conditions to synchronize a subsystem of one chaotic system with a separate chaotic system by sending a signal from the chaotic system to the subsystem. We describe here the conditions necessary for synchronization and demonstrate synchronization… (More)

- Louis M. Pecora, Thomas L. Carroll, Gregg A. Johnson, Douglas J. Mar, James F. Heagy
- 1997

The field of chaotic synchronization has grown considerably since its advent in 1990. Several subdisciplines and ‘‘cottage industries’’ have emerged that have taken on bona fide lives of their own. Our purpose in this paper is to collect results from these various areas in a review article format with a tutorial emphasis. Fundamentals of chaotic… (More)

- Louis M. Pecora, Thomas L. Carroll, Gregg Johnson, Doug Mar, Kenneth S. Fink
- I. J. Bifurcation and Chaos
- 2000

- Louis M Pecora, Francesco Sorrentino, Aaron M Hagerstrom, Thomas E Murphy, Rajarshi Roy
- Nature communications
- 2014

Synchronization is of central importance in power distribution, telecommunication, neuronal and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these clusters or understand the conditions under which they form. Here we present a new framework and develop techniques for the… (More)

- Liang Huang, Qingfei Chen, Ying-Cheng Lai, Louis M Pecora
- Physical review. E, Statistical, nonlinear, and…
- 2009

Master-stability functions (MSFs) are fundamental to the study of synchronization in complex dynamical systems. For example, for a coupled oscillator network, a necessary condition for synchronization to occur is that the MSF at the corresponding normalized coupling parameters be negative. To understand the typical behaviors of the MSF for various chaotic… (More)

Title of dissertation: SYNCHRONIZATION AND PREDICTION OF CHAOTIC DYNAMICS ON NETWORKS OF OPTOELECTRONIC OSCILLATORS Adam Brent Cohen, Doctor of Philosophy, 2011 Dissertation directed by: Professor Rajarshi Roy Department of Physics The subject of this thesis is the exploration of chaotic synchronization for novel applications including time-series… (More)

We introduce the theory of identical or complete synchronization of identical oscillators in arbitrary networks. In addition, we introduce several graph theory concepts and results that augment the synchronization theory and tie is closely to random, semirandom, and regular networks. We then use the combined theories to explore and compare three types of… (More)

- Louis M Pecora, Linda Moniz, Jonathan Nichols, Thomas L Carroll
- Chaos
- 2007

In the analysis of complex, nonlinear time series, scientists in a variety of disciplines have relied on a time delayed embedding of their data, i.e., attractor reconstruction. The process has focused primarily on intuitive, heuristic, and empirical arguments for selection of the key embedding parameters, delay and embedding dimension. This approach has… (More)