23,809 research outputs found
Controlling edge dynamics in complex networks
The interaction of distinct units in physical, social, biological and
technological systems naturally gives rise to complex network structures.
Networks have constantly been in the focus of research for the last decade,
with considerable advances in the description of their structural and dynamical
properties. However, much less effort has been devoted to studying the
controllability of the dynamics taking place on them. Here we introduce and
evaluate a dynamical process defined on the edges of a network, and demonstrate
that the controllability properties of this process significantly differ from
simple nodal dynamics. Evaluation of real-world networks indicates that most of
them are more controllable than their randomized counterparts. We also find
that transcriptional regulatory networks are particularly easy to control.
Analytic calculations show that networks with scale-free degree distributions
have better controllability properties than uncorrelated networks, and
positively correlated in- and out-degrees enhance the controllability of the
proposed dynamics.Comment: Preprint. 24 pages, 4 figures, 2 tables. Source code available at
http://github.com/ntamas/netctr
Control and Synchronization of Neuron Ensembles
Synchronization of oscillations is a phenomenon prevalent in natural, social,
and engineering systems. Controlling synchronization of oscillating systems is
motivated by a wide range of applications from neurological treatment of
Parkinson's disease to the design of neurocomputers. In this article, we study
the control of an ensemble of uncoupled neuron oscillators described by phase
models. We examine controllability of such a neuron ensemble for various phase
models and, furthermore, study the related optimal control problems. In
particular, by employing Pontryagin's maximum principle, we analytically derive
optimal controls for spiking single- and two-neuron systems, and analyze the
applicability of the latter to an ensemble system. Finally, we present a robust
computational method for optimal control of spiking neurons based on
pseudospectral approximations. The methodology developed here is universal to
the control of general nonlinear phase oscillators.Comment: 29 pages, 6 figure
On Submodularity and Controllability in Complex Dynamical Networks
Controllability and observability have long been recognized as fundamental
structural properties of dynamical systems, but have recently seen renewed
interest in the context of large, complex networks of dynamical systems. A
basic problem is sensor and actuator placement: choose a subset from a finite
set of possible placements to optimize some real-valued controllability and
observability metrics of the network. Surprisingly little is known about the
structure of such combinatorial optimization problems. In this paper, we show
that several important classes of metrics based on the controllability and
observability Gramians have a strong structural property that allows for either
efficient global optimization or an approximation guarantee by using a simple
greedy heuristic for their maximization. In particular, the mapping from
possible placements to several scalar functions of the associated Gramian is
either a modular or submodular set function. The results are illustrated on
randomly generated systems and on a problem of power electronic actuator
placement in a model of the European power grid.Comment: Original arXiv version of IEEE Transactions on Control of Network
Systems paper (Volume 3, Issue 1), with a addendum (located in the ancillary
documents) that explains an error in a proof of the original paper and
provides a counterexample to the corresponding resul
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