Dynamic Systems Commons^™

Latent Space Models For Temporal Networks, Jasper Alt

Systems Science Friday Noon Seminar Series

In many contexts we may expect the structure of networks to be derived from some kind of abstract distance between actors. We refer to this phenomenon as homophily: like nodes connect to like. For example, people with similar beliefs may be more likely to form social relations.

We formalize this notion by positioning the nodes in a latent space representing the possible values of the homophilous attributes. Realistically, we should expect latent attributes like beliefs to change over time in some nontrivial way, and the structures of temporal networks to evolve accordingly. We introduce a model of latent space dynamics …

Transients In The Synchronization Of Asymmetrically Coupled Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.

Dynamics Of Locally Coupled Oscillators With Next-Nearest-Neighbor Interaction, J. Herbrych, A. G. Chazirakis, N. Christakis, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

A theoretical description of decentralized dynamics within linearly coupled, one-dimensional oscillators (agents) with up to next-nearest-neighbor interaction is given. Conditions for stability of such system are presented. Our results indicate that the stable systems have response that grow at least linearly in the system size. We give criteria when this is the case. The dynamics of these systems can be described with traveling waves with strong damping in the high frequencies. Depending on the system parameters, two types of solutions have been found: damped oscillations and reflectionless waves. The latter is a novel result and a feature of systems with …

Effect Of Network Structure On The Stability Margin Of Large Vehicle With Distributed Control, He Hao, Prabir Barooah, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We study the problem of distributed control of a large network of double-integrator agents to maintain a rigid formation. A few lead vehicles are given information on the desired trajectory of the formation; while every other vehicle uses linear controller which only depends on relative position and velocity from a few other vehicles, which are called its neighbors. A predetermined information graph defines the neighbor relationships. We limit our attention to information graphs that are D-dimensional lattices, and examine the stability margin of the closed loop, which is measured by the real part of the least stable eigenvalue of …

Entropy Measures In Input-Output Analysis, Martin Zwick, Abbas Heiat

Complex Systems Faculty Publications and Presentations

Applications of Shannon's entropy measure to the matrices of technical and interdependence coefficients, to the final demand vector, and to other aspects of input- output tables are proposed. These entropy measures serve as indices of different types of economic diversity. The relevance of such indices for economic planning and for analyses of economic structural complexity and development is discussed.