21 research outputs found
Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings
The effects of symmetry on the dynamics of antigenic variation
In the studies of dynamics of pathogens and their interactions with a host
immune system, an important role is played by the structure of antigenic
variants associated with a pathogen. Using the example of a model of antigenic
variation in malaria, we show how many of the observed dynamical regimes can be
explained in terms of the symmetry of interactions between different antigenic
variants. The results of this analysis are quite generic, and have wider
implications for understanding the dynamics of immune escape of other
parasites, as well as for the dynamics of multi-strain diseases.Comment: 21 pages, 4 figures; J. Math. Biol. (2012), Online Firs
Efficient Network Reconstruction from Dynamical Cascades Identifies Small-World Topology of Neuronal Avalanches
Cascading activity is commonly found in complex systems with directed
interactions such as metabolic networks, neuronal networks, or disease spreading
in social networks. Substantial insight into a system's organization
can be obtained by reconstructing the underlying functional network architecture
from the observed activity cascades. Here we focus on Bayesian approaches and
reduce their computational demands by introducing the Iterative Bayesian (IB)
and Posterior Weighted Averaging (PWA) methods. We introduce a special case of
PWA, cast in nonparametric form, which we call the normalized count (NC)
algorithm. NC efficiently reconstructs random and small-world functional network
topologies and architectures from subcritical, critical, and supercritical
cascading dynamics and yields significant improvements over commonly used
correlation methods. With experimental data, NC identified a functional and
structural small-world topology and its corresponding traffic in cortical
networks with neuronal avalanche dynamics
Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings
We study the problem of controlled network synchronization of coupled semipassive systems in the case when the outputs (the coupling variables) and the inputs are subject to constant time-delays (as it is often the case in a networked context). Predictor-based dynamic output feedback controllers are proposed to interconnect the systems on a given network. Using Lyapunov-Krasovskii functionals and the notion of semipassivity, we prove that under some mild assumptions, the solutions of the interconnected systems are globally ultimately bounded. Sufficient conditions on the systems to be interconnected, on the network topology, on the coupling dynamics, and on the time-delays that guarantee global state synchronization are derived. A local analysis is provided, in which we compare the performance of our predictor-based control scheme against the existing static diffusive couplings available in the literature. We show (locally) that the time-delay that can be induced to the network may be increased by including the predictors in the loop. The results are illustrated by computer simulations of coupled Hindmarsh-Rose neurons