22,008 research outputs found
A Time-Varying Complex Dynamical Network Model And Its Controlled Synchronization Criteria
Today, complex networks have attracted increasing attention from various
fields of science and engineering. It has been demonstrated that many complex
networks display various synchronization phenomena. In this paper, we introduce
a time-varying complex dynamical network model. We then further investigate its
synchronization phenomenon and prove several network synchronization theorems.
Especially, we show that synchronization of such a time-varying dynamical
network is completely determined by the inner-coupling matrix, and the
eigenvalues and the corresponding eigenvectors of the coupling configuration
matrix of the network.Comment: 13 page
Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks
We study projective-anticipating, projective, and projective-lag
synchronization of time-delayed chaotic systems on random networks. We relax
some limitations of previous work, where projective-anticipating and
projective-lag synchronization can be achieved only on two coupled chaotic
systems. In this paper, we can realize projective-anticipating and
projective-lag synchronization on complex dynamical networks composed by a
large number of interconnected components. At the same time, although previous
work studied projective synchronization on complex dynamical networks, the
dynamics of the nodes are coupled partially linear chaotic systems. In this
paper, the dynamics of the nodes of the complex networks are time-delayed
chaotic systems without the limitation of the partial-linearity. Based on the
Lyapunov stability theory, we suggest a generic method to achieve the
projective-anticipating, projective, and projective-lag synchronization of
time-delayed chaotic systems on random dynamical networks and find both the
existence and sufficient stability conditions. The validity of the proposed
method is demonstrated and verified by examining specific examples using Ikeda
and Mackey-Glass systems on Erdos-Renyi networks.Comment: 14 pages, 6 figure
Neuronal synchrony: peculiarity and generality
Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their “dynamical repertoire” includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale
Explosive Synchronization Transitions in Scale-free Networks
The emergence of explosive collective phenomena has recently attracted much
attention due to the discovery of an explosive percolation transition in
complex networks. In this Letter, we demonstrate how an explosive transition
shows up in the synchronization of complex heterogeneous networks by
incorporating a microscopic correlation between the structural and the
dynamical properties of the system. The characteristics of this explosive
transition are analytically studied in a star graph reproducing the results
obtained in synthetic scale-free networks. Our findings represent the first
abrupt synchronization transition in complex networks thus providing a deeper
understanding of the microscopic roots of explosive critical phenomena.Comment: 6 pages and 5 figures. To appear in Physical Review Letter
Bounding network spectra for network design
The identification of the limiting factors in the dynamical behavior of
complex systems is an important interdisciplinary problem which often can be
traced to the spectral properties of an underlying network. By deriving a
general relation between the eigenvalues of weighted and unweighted networks,
here I show that for a wide class of networks the dynamical behavior is tightly
bounded by few network parameters. This result provides rigorous conditions for
the design of networks with predefined dynamical properties and for the
structural control of physical processes in complex systems. The results are
illustrated using synchronization phenomena as a model process.Comment: 17 pages, 4 figure
Network centrality: an introduction
Centrality is a key property of complex networks that influences the behavior
of dynamical processes, like synchronization and epidemic spreading, and can
bring important information about the organization of complex systems, like our
brain and society. There are many metrics to quantify the node centrality in
networks. Here, we review the main centrality measures and discuss their main
features and limitations. The influence of network centrality on epidemic
spreading and synchronization is also pointed out in this chapter. Moreover, we
present the application of centrality measures to understand the function of
complex systems, including biological and cortical networks. Finally, we
discuss some perspectives and challenges to generalize centrality measures for
multilayer and temporal networks.Comment: Book Chapter in "From nonlinear dynamics to complex systems: A
Mathematical modeling approach" by Springe
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
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