Symmetries of complex networks: dynamics and control
Abstract
A large body of literature has investigated the structure and functions of complex dynamicalnetworks. Typical examples of dynamics that have been considered include epidemics, trafficand congestion, synchronization, evolutionary games, cascading failures, et cetera. Applicationsof these studies are relevant to biological networks, such as food webs, neuronal circuits, andgene-regulatory networks, as it appears Nature has often exploited network structures to organizeitself at many different levels and scales. An important feature of these networks is the presenceof symmetries of the underlying network topology, which so far has remained to some extentunexplored, with some exceptions.Recently, considerable research efforts have been devoted to analyze controllability and observabilityof complex dynamical networks. We start from two important observations, which providethe motivation for our research: the first one is that in real applications involving large complex networks,achieving control over all the network nodes is often unfeasible and ultimately unnecessary;what appears to be a more reasonable goal is that of affecting a subset of the network nodes that arechosen as the target of the control action [1] (for example, genes involved in a particular pathwayin a gene regulatory network). The second one is that in several applications (think for example ofbiological networks) it is often important to exert the control action by injecting the least amountof energy in the system. The theory of optimal control allows to compute the control action whichminimizes the expenditure of energy. Even if the system deviates from its model, a calculation ofthe minimum control energy can provide an important indication on the order of magnitude for theenergy required by the control action.Controlling complex networks is a promising and broad research area with applications rangingfrom social systems (control of a terrorists network) to biological systems (control of gene regulatorynetworks and cell signaling networks) and technological systems (control of a spacecraft network).For all these examples, the underlying network symmetries affect both the dynamics and our abilityto exert the control action. We investigate the interplay between the network structure, in particularthe symmetries, and the network dynamics [2]. Our approach will be tested in several controlschemes with applications to cluster consensus, control of spacecraft dynamics, and control ofautophagy levels in cell signaling networks. Both the questions of controllability and of designingefficient and minimally invasive control strategies will be addressed.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141612637
Entities
People
- Francesco Sorrentino
Organizations
- Office of Naval Research
- United States Navy
- University of New Mexico