46 research outputs found
Synchronization of interconnected networks: the role of connector nodes
In this Letter we identify the general rules that determine the
synchronization properties of interconnected networks. We study analytically,
numerically and experimentally how the degree of the nodes through which two
networks are connected influences the ability of the whole system to
synchronize. We show that connecting the high-degree (low-degree) nodes of each
network turns out to be the most (least) effective strategy to achieve
synchronization. We find the functional relation between synchronizability and
size for a given network-of-networks, and report the existence of the optimal
connector link weights for the different interconnection strategies. Finally,
we perform an electronic experiment with two coupled star networks and conclude
that the analytical results are indeed valid in the presence of noise and
parameter mismatches.Comment: Accepted for publication in Physical Review Letters. Main text: 5
pages, 4 figures. Supplemental material: 8 pages, 3 figure
Relay synchronization in multiplex networks
Relay (or remote) synchronization between two not directly connected
oscillators in a network is an important feature allowing distant coordination.
In this work, we report a systematic study of this phenomenon in multiplex
networks, where inter-layer synchronization occurs between distant layers
mediated by a relay layer that acts as a transmitter. We show that this
transmission can be extended to higher order relay configurations, provided
symmetry conditions are preserved. By first order perturbative analysis, we
identify the dynamical and topological dependencies of relay synchronization in
a multiplex. We find that the relay synchronization threshold is considerably
reduced in a multiplex configuration, and that such synchronous state is mostly
supported by the lower degree nodes of the outer layers, while hubs can be
de-multiplexed without affecting overall coherence. Finally, we experimentally
validated the analytical and numerical findings by means of a multiplex of
three layers of electronic circuits.the analytical and numerical findings by
means of a multiplex of three layers of electronic circuits
Explosive first-order transition to synchrony in networked chaotic oscillators
Critical phenomena in complex networks, and the emergence of dynamical abrupt
transitions in the macroscopic state of the system are currently a subject of
the outmost interest. We report evidence of an explosive phase synchronization
in networks of chaotic units. Namely, by means of both extensive simulations of
networks made up of chaotic units, and validation with an experiment of
electronic circuits in a star configuration, we demonstrate the existence of a
first order transition towards synchronization of the phases of the networked
units. Our findings constitute the first prove of this kind of synchronization
in practice, thus opening the path to its use in real-world applications.Comment: Phys. Rev. Lett. in pres
Experimental implementation of maximally synchronizable networks
Maximally synchronizable networks (MSNs) are acyclic directed networks that maximize synchronizability. In this paper, we investigate the feasibility of transforming networks of coupled oscillators into their corresponding MSNs. By tuning the weights of any given network so as to reach the lowest possible eigenratio lambdaN/lambda2, the synchronized state is guaranteed to be maintained across the longest possible range of coupling strengths. We check the robustness of the resulting MSNs with an experimental implementation of a network of nonlinear electronic oscillators and study the propagation of the synchronization errors through the network. Importantly, a method to study the effects of topological uncertainties on the synchronizability is proposed and explored both theoretically and experimentally.The authors acknowledge J.L. Echenausía-Monroy, V.P. Vera-Ávila, J. Moreno de León, C. Hapo and P.L. del Barrio for assistance in the laboratory, and the support of MINECO (FIS2012-38949-C03-01 and FIS2013-41057-P). One anonymous referee is acknowledged for having provided valuable advice that has influenced our understanding of the origin of the propagation of the synchronization error, and helped us improve the manuscript in several ways. The authors also acknowledge the computational resources, facilities and assistance provided by the Centro computazionale di RicErca sui Sistemi COmplessi (CRESCO) of the Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA). R.S.E. acknowledges Universidad de Guadalajara, CULagos (Mexico) for financial support (PRO-SNI-2015/228069, PROINPEP/005/2014, UDG-CONACyT/I010/163/2014) and CONACyT (Becas Mixtas MZO2015/290842). D.-U. Hwang acknowledges National Institute for Mathematical Sciences (NIMS) funded by the Ministry of Science, ICT & Future Planning (A21501-3)
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)
Observability of dynamical networks from graphic and symbolic approaches
A dynamical network, a graph whose nodes are dynamical systems, is usually
characterized by a large dimensional space which is not always accesible due to
the impossibility of measuring all the variables spanning the state space.
Therefore, it is of the utmost importance to determine a reduced set of
variables providing all the required information for non-ambiguously
distinguish its different states. Inherited from control theory, one possible
approach is based on the use of the observability matrix defined as the
Jacobian matrix of the change of coordinates between the original state space
and the space reconstructed from the measured variables. The observability of a
given system can be accurately assessed by symbolically computing the
complexity of the determinant of the observability matrix and quantified by
symbolic observability coefficients. In this work, we extend the symbolic
observability, previously developed for dynamical systems, to networks made of
coupled -dimensional node dynamics (). From the observability of the
node dynamics, the coupling function between the nodes, and the adjacency
matrix, it is indeed possible to construct the observability of a large network
with an arbitrary topology.Comment: 12 pages, 4 figures made from 12 eps file
The physics of spreading processes in multilayer networks
The study of networks plays a crucial role in investigating the structure,
dynamics, and function of a wide variety of complex systems in myriad
disciplines. Despite the success of traditional network analysis, standard
networks provide a limited representation of complex systems, which often
include different types of relationships (i.e., "multiplexity") among their
constituent components and/or multiple interacting subsystems. Such structural
complexity has a significant effect on both dynamics and function. Throwing
away or aggregating available structural information can generate misleading
results and be a major obstacle towards attempts to understand complex systems.
The recent "multilayer" approach for modeling networked systems explicitly
allows the incorporation of multiplexity and other features of realistic
systems. On one hand, it allows one to couple different structural
relationships by encoding them in a convenient mathematical object. On the
other hand, it also allows one to couple different dynamical processes on top
of such interconnected structures. The resulting framework plays a crucial role
in helping achieve a thorough, accurate understanding of complex systems. The
study of multilayer networks has also revealed new physical phenomena that
remain hidden when using ordinary graphs, the traditional network
representation. Here we survey progress towards attaining a deeper
understanding of spreading processes on multilayer networks, and we highlight
some of the physical phenomena related to spreading processes that emerge from
multilayer structure.Comment: 25 pages, 4 figure
Controlling multistability in a vibro-impact capsule system
This is the final version of the article. Available from Springer Verlag via the DOI in this record.This work concerns the control of multistability in a vibro-impact capsule system driven by a harmonic excitation. The capsule is able to move forward and backward in a rectilinear direction, and the main objective of this work is to control such motion in the presence of multiple coexisting periodic solutions. A position feedback controller is employed in this study, and our numerical investigation demonstrates that the proposed control method gives rise to a dynamical scenario with two coexisting solutions, corresponding to forward and backward progression. Therefore, the motion direction of the system can be controlled by suitably perturbing its initial conditions, without altering the system parameters. To study the robustness of this control method, we apply numerical continuation methods in order to identify a region in the parameter space in which the proposed controller can be applied. For this purpose, we employ the MATLAB-based numerical platform COCO, which supports the continuation and bifurcation detection of periodic orbits of non-smooth dynamical systems.The second author has been supported by a Georg Forster Research Fellowship granted by the Alexander von Humboldt Foundation, Germany. The authors would like to thank Dr. Haibo Jiang for stimulating discussions and comments on this work