Synchronization of dynamical networks with nonidentical nodes: Criteria and control

This paper presents a framework for global synchronization of dynamical networks with nonidentical nodes. Several criteria for synchronization are given using free matrices for both cases of synchronizing to a common equilibrium solution of all isolated nodes and synchronizing to the average state trajectory. These criteria can be viewed as generalizations of the master stability function method for local synchronization of networks with identical nodes to the case of nonidentical nodes. The controlled synchronization problem is also studied. The control action, which is subject to certain constraints, is viewed as reorganization of the connection topology of the network. Synchronizability conditions via control are put forward. The synchronizing controllers can be obtained by solving an optimization problem.published_or_final_versio

Synchronizability of random rectangular graphs

Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the network becomes harder to synchronize. The synchronization processing behavior of a RRG network of chaotic Lorenz system nodes is numerically investigated, showing complete consistence with the theoretical results

Module hierarchy and centralisation in the anatomy and dynamics of human cortex

Systems neuroscience has recently unveiled numerous fundamental features of the macroscopic architecture of the human brain, the connectome, and we are beginning to understand how characteristics of brain dynamics emerge from the underlying anatomical connectivity. The current work utilises complex network analysis on a high-resolution structural connectivity of the human cortex to identify generic organisation principles, such as centralised, modular and hierarchical properties, as well as specific areas that are pivotal in shaping cortical dynamics and function. After confirming its small-world and modular architecture, we characterise the cortex’ multilevel modular hierarchy, which appears to be reasonably centralised towards the brain’s strong global structural core. The potential functional importance of the core and hub regions is assessed by various complex network metrics, such as integration measures, network vulnerability and motif spectrum analysis. Dynamics facilitated by the large-scale cortical topology is explored by simulating coupled oscillators on the anatomical connectivity. The results indicate that cortical connectivity appears to favour high dynamical complexity over high synchronizability. Taking the ability to entrain other brain regions as a proxy for the threat posed by a potential epileptic focus in a given region, we also show that epileptic foci in topologically more central areas should pose a higher epileptic threat than foci in more peripheral areas. To assess the influence of macroscopic brain anatomy in shaping global resting state dynamics on slower time scales, we compare empirically obtained functional connectivity data with data from simulating dynamics on the structural connectivity. Despite considerable micro-scale variability between the two functional connectivities, our simulations are able to approximate the profile of the empirical functional connectivity. Our results outline the combined characteristics a hierarchically modular and reasonably centralised macroscopic architecture of the human cerebral cortex, which, through these topological attributes, appears to facilitate highly complex dynamics and fundamentally shape brain function

Design of oscillator networks with enhanced synchronization tolerance against noise

Can synchronization properties of a network of identical oscillators in the presence of noise be improved through appropriate rewiring of its connections? What are the optimal network architectures for a given total number of connections? We address these questions by running the optimization process, using the stochastic Markov Chain Monte Carlo method with replica exchange, to design the networks of phase oscillators with the increased tolerance against noise. As we find, the synchronization of a network, characterized by the Kuramoto order parameter, can be increased up to 40 %, as compared to that of the randomly generated networks, when the optimization is applied. Large ensembles of optimized networks are obtained and their statistical properties are investigated.Comment: 9 pages, 8 figure

Enhancing the stability of the synchronization of multivariable coupled oscillators

Synchronization processes in populations of identical networked oscillators are the focus of intense studies in physical, biological, technological, and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal coupling transference that maximizes the stability of the synchronous state in a network of Rössler-like oscillators. Finally, we design an experimental implementation (using nonlinear electronic circuits) which grounds the robustness of the theoretical predictions against parameter mismatches, as well as against intrinsic noise of the system.Support from Spanish Ministry of Economy and Competitiveness through Projects No. FIS2011-25167, No. FIS2012-38266, and No. FIS2013-41057-P is also acknowledged. A.A. and J.G.G. acknowledge supportfrom the EC FET-Proactive Projects PLEXMATH (GrantNo. 317614) and MULTIPLEX (Grant No. 317532). J.G.G. acknowledges support from MINECO through the Ramón y Cajal program, the Comunidad de Aragón (Grupo FENOL), and the Brazilian CNPq through the PVE project of the Ciencia Sem Fronteiras program. A.A. acknowledges ICREA Academia and the James S. McDonnell Foundation. R.S.E. ac-knowledges Universidad de Guadalajara, CULagos (Mexico) for financial support (OP/PIFI-2013-14MSU0010Z-17-04,PROINPEP-RG/005/2014, UDG-CONACyT/I010/163/2014) and CONACyT (Becas Mixtas MZO2015/290842)

Bounded H∞ synchronization and state estimation for discrete time-varying stochastic complex for discrete time-varying stochastic complex networks over a finite horizon

Copyright [2011] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, new synchronization and state estimation problems are considered for an array of coupled discrete time-varying stochastic complex networks over a finite horizon. A novel concept of bounded H∞ synchronization is proposed to handle the time-varying nature of the complex networks. Such a concept captures the transient behavior of the time-varying complex network over a finite horizon, where the degree of bounded synchronization is quantified in terms of the H∞-norm. A general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. By utilizing a timevarying real-valued function and the Kronecker product, criteria are established that ensure the bounded H∞ synchronization in terms of a set of recursive linear matrix inequalities (RLMIs), where the RLMIs can be computed recursively by employing available MATLAB toolboxes. The bounded H∞ state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that, over a finite horizon, the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level. Again, an RLMI approach is developed for the state estimation problem. Finally, two simulation examples are exploited to show the effectiveness of the results derived in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council of U.K. under Grant GR/S27658/01, the National Natural Science Foundation of China under Grant 61028008 and Grant 60974030, the National 973 Program of China under Grant 2009CB320600, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany

Cigarette Smoke Up-regulates PDE3 and PDE4 to Decrease cAMP in Airway Cells

BACKGROUND AND PURPOSE: 3', 5'-cyclic adenosine monophosphate (cAMP) is a central second messenger that broadly regulates cell function and can underpin pathophysiology. In chronic obstructive pulmonary disease (COPD), a lung disease primarily provoked by cigarette smoke (CS), the induction of cAMP-dependent pathways, via inhibition of hydrolyzing phosphodiesterases (PDEs), is a prime therapeutic strategy. Mechanisms that disrupt cAMP signaling in airway cells, in particular regulation of endogenous PDEs are poorly understood. EXPERIMENTAL APPROACH: We used a novel Förster resonance energy transfer (FRET) based cAMP biosensor in mouse in vivo, ex vivo precision cut lung slices (PCLS), and in human in vitro cell models to track the effects of CS exposure. KEY RESULTS: Under fenoterol stimulated conditions, FRET responses to cilostamide were significantly increased in in vivo, ex vivo PCLS exposed to CS and in human airway smooth muscle cells exposed to CS extract. FRET signals to rolipram were only increased in the in vivo CS model. Under basal conditions, FRET responses to cilostamide and rolipram were significantly increased in in vivo, ex vivo PCLS exposed to CS. Elevated FRET signals to rolipram correlated with a protein upregulation of PDE4 subtypes. In ex vivo PCLS exposed to CS extract, rolipram reversed downregulation of ciliary beating frequency, whereas only cilostamide significantly increased airway relaxation of methacholine pre-contracted airways. CONCLUSION AND IMPLICATIONS: We show that CS upregulates expression and activity of both PDE3 and PDE4, which regulate real-time cAMP dynamics. These mechanisms determine the availability of cAMP and can contribute to CS-induced pulmonary pathophysiology

Multi-Agent Systems and Complex Networks: Review and Applications in Systems Engineering

Systems engineering is an ubiquitous discipline of Engineering overlapping industrial, chemical, mechanical, manufacturing, control, software, electrical, and civil engineering. It provides tools for dealing with the complexity and dynamics related to the optimisation of physical, natural, and virtual systems management. This paper presents a review of how multi-agent systems and complex networks theory are brought together to address systems engineering and management problems. The review also encompasses current and future research directions both for theoretical fundamentals and applications in the industry. This is made by considering trends such as mesoscale, multiscale, and multilayer networks along with the state-of-art analysis on network dynamics and intelligent networks. Critical and smart infrastructure, manufacturing processes, and supply chain networks are instances of research topics for which this literature review is highly relevant

Structural engineering of evolving complex dynamical networks

Networks are ubiquitous in nature and many natural and man-made systems can be modelled as networked systems. Complex networks, systems comprising a number of nodes that are connected through edges, have been frequently used to model large-scale systems from various disciplines such as biology, ecology, and engineering. Dynamical systems interacting through a network may exhibit collective behaviours such as synchronisation, consensus, opinion formation, flocking and unusual phase transitions. Evolution of such collective behaviours is highly dependent on the structure of the interaction network. Optimisation of network topology to improve collective behaviours and network robustness can be achieved by intelligently modifying the network structure. Here, it is referred to as "Engineering of the Network". Although coupled dynamical systems can develop spontaneous synchronous patterns if their coupling strength lies in an appropriate range, in some applications one needs to control a fraction of nodes, known as driver nodes, in order to facilitate the synchrony. This thesis addresses the problem of identifying the set of best drivers, leading to the best pinning control performance. The eigen-ratio of the augmented Laplacian matrix, that is the largest eigenvalue divided by the second smallest one, is chosen as the controllability metric. The approach introduced in this thesis is to obtain the set of optimal drivers based on sensitivity analysis of the eigen-ratio, which requires only a single computation of the eigenvector associated with the largest eigenvalue, and thus is applicable for large-scale networks. This leads to a new "controllability centrality" metric for each subset of nodes. Simulation results reveal the effectiveness of the proposed metric in predicting the most important driver(s) correctly.     Interactions in complex networks might also facilitate the propagation of undesired effects, such as node/edge failure, which may crucially affect the performance of collective behaviours. In order to study the effect of node failure on network synchronisation, an analytical metric is proposed that measures the effect of a node removal on any desired eigenvalue of the Laplacian matrix. Using this metric, which is based on the local multiplicity of each eigenvalue at each node, one can approximate the impact of any node removal on the spectrum of a graph. The metric is computationally efficient as it only needs a single eigen-decomposition of the Laplacian matrix. It also provides a reliable approximation for the "Laplacian energy" of a network. Simulation results verify the accuracy of this metric in networks with different topologies. This thesis also considers formation control as an application of network synchronisation and studies the "rigidity maintenance" problem, which is one of the major challenges in this field. This problem is to preserve the rigidity of the sensing graph in a formation during motion, taking into consideration constraints such as line-of-sight requirements, sensing ranges and power limitations. By introducing a "Lattice of Configurations" for each node, a distributed rigidity maintenance algorithm is proposed to preserve the rigidity of the sensing network when failure in a sensing link would result in loss of rigidity. The proposed algorithm recovers rigidity by activating, almost always, the minimum number of new sensing links and considers real-time constraints of practical formations. A sufficient condition for this problem is proved and tested via numerical simulations. Based on the above results, a number of other areas and applications of network dynamics are studied and expounded upon in this thesis

Network Formation and Dynamics under Economic Constraints

Networks describe a broad range of systems across a wide variety of topics from social and economic interactions over technical infrastructures such as power grids and the internet to biological contexts such as food webs or neural networks. A number of large scale failures and events in these interconnected systems in recent years has shown that understanding the behavior of individual units of these networks is not necessarily sufficient to handle the increasing complexity of these systems. Many theoretical models have been studied to understand the fundamental mechanisms underlying the formation and function of networked systems and a general framework was developed to describe and understand networked systems. However, most of these models ignore a constraint that affects almost all realistic systems: limited resources. In this thesis I study the effects of economic constraints, such as a limited budget or cost minimization, both on the control of network formation and dynamics as well as on network formation itself. I introduce and analyze a new coupling scheme for coupled dynamical systems, showing that synchronization of chaotic units can be enhanced by restricting the interactions based on the states of the individual units, thus saving interactions costs. This new interaction scheme guarantees synchronizability of arbitrary networks of coupled chaotic oscillators, independent of the network topology even with strongly limited interactions. I then propose a new order parameter to measure the degree of phase coherence of networks of coupled phase oscillators. This new order parameter accurately describes the phase coherence in all stages of incoherent movement, partial and full phase locking up to full synchrony. Importantly, I analytically relate this order parameter directly to the stability of the phase locked state. In the second part, I consider the formation of networks under economic constraints from two different points of view. First I study the effects of explicitly limited resources on the control of random percolation, showing that optimal control can have undesired side effects. Specifically, maximal delay of percolation with a limited budget results in a discontinuous percolation transition, making the transition itself uncontrollable in the sense that a single link can have a macroscopic effect on the connectivity. Finally, I propose a model where network formation is driven by cost minimization of the individual nodes in the network. Based on a simple economically motivated supply problem, the resulting network structure is given as the solution of a large number of individual but interaction optimization problem. I show that these network states directly correspond to the final states of a local percolation algorithm and analyze the effects of local optimization on the network formation process. Overall, I reveal mechanisms and phenomena introduced by these economic constraints that are typically not considered in the standard models, showing that economic constraints can strongly alter the formation and function of networked systems. Thereby, I extend the theoretical understanding that we have of networked systems to economic considerations. I hope that this thesis enables better prediction and control networked systems in realistic settings