93,411 research outputs found
Spectral Network Principle for Frequency Synchronization in Repulsive Laser Networks
Network synchronization of lasers is critical for reaching high-power levels
and for effective optical computing. Yet, the role of network topology for the
frequency synchronization of lasers is not well understood. Here, we report our
significant progress toward solving this critical problem for networks of
heterogeneous laser model oscillators with repulsive coupling. We discover a
general approximate principle for predicting the onset of frequency
synchronization from the spectral knowledge of a complex matrix representing a
combination of the signless Laplacian induced by repulsive coupling and a
matrix associated with intrinsic frequency detuning. We show that the gap
between the two smallest eigenvalues of the complex matrix generally controls
the coupling threshold for frequency synchronization. In stark contrast with
Laplacian networks, we demonstrate that local rings and all-to-all networks
prevent frequency synchronization, whereas full bipartite networks have optimal
synchronization properties. Beyond laser models, we show that, with a few
exceptions, the spectral principle can be applied to repulsive Kuramoto
networks. Our results may provide guidelines for optimal designs of scalable
laser networks capable of achieving reliable synchronization
Local Dirac Synchronization on Networks
We propose Local Dirac Synchronization which uses the Dirac operator to
capture the dynamics of coupled nodes and link signals on an arbitrary network.
In Local Dirac Synchronization, the harmonic modes of the dynamics oscillate
freely while the other modes are interacting non-linearly, leading to a
collectively synchronized state when the coupling constant of the model is
increased. Local Dirac Synchronization is characterized by discontinuous
transitions and the emergence of a rhythmic coherent phase. In this rhythmic
phase, one of the two complex order parameters oscillates in the complex plane
at a slow frequency (called emergent frequency) in the frame in which the
intrinsic frequencies have zero average. Our theoretical results obtained
within the annealed approximation are validated by extensive numerical results
on fully connected networks and sparse Poisson and scale-free networks. Local
Dirac Synchronization on both random and real networks, such as the connectome
of Caenorhabditis Elegans, reveals the interplay between topology (Betti
numbers and harmonic modes) and non-linear dynamics. This unveils how topology
might play a role in the onset of brain rhythms.Comment: 17 pages, 16 figures + appendice
Formation of Modularity in a Model of Evolving Networks
Modularity structures are common in various social and biological networks.
However, its dynamical origin remains an open question. In this work, we set up
a dynamical model describing the evolution of a social network. Based on the
observations of real social networks, we introduced a link-creating/deleting
strategy according to the local dynamics in the model. Thus the coevolution of
dynamics and topology naturally determines the network properties. It is found
that for a small coupling strength, the networked system cannot reach any
synchronization and the network topology is homogeneous. Interestingly, when
the coupling strength is large enough, the networked system spontaneously forms
communities with different dynamical states. Meanwhile, the network topology
becomes heterogeneous with modular structures. It is further shown that in a
certain parameter regime, both the degree and the community size in the formed
network follow a power-law distribution, and the networks are found to be
assortative. These results are consistent with the characteristics of many
empirical networks, and are helpful to understand the mechanism of formation of
modularity in complex networks.Comment: 6 pages, 4 figur
Self-regulation of a network of Kuramoto oscillators
Treballs Finals de Màster en Física dels Sistemes Complexos i Biofísica, Facultat de Física, Universitat de Barcelona. Curs: 2022-2023. Tutors: Albert Díaz-Guilera, Jordi Soriano FraderaPersistent global synchronization of a neuronal network is considered a pathological, undesired state. Such as synchronization is often caused by the loss of neurons that regulate network dynamics, or cells that assist these neurons such as glial cells. Here we propose a self-regulation model in the framework of complex networks in which we assume that, for sake of simplicity, glial cells prevent the over synchronization of the neuronal network. We have considered a brain-like network characterized by a modular organization combined with a dynamic description of the nodes as Kuramoto oscillators. We have applied a self-regulation mechanism to keep local synchronization while avoiding global synchronization at the same time. To do so, we have added self-regulation to the system by switching off for a certain period of time a selection of edges that link nodes showing a synchronization above a certain threshold. Despite the simplicity of the approximation, our results
show that it is possible to maintain a high local synchronization (module level) while keeping low the global one. In addition, characteristic dynamic patterns have been observed when analysing synchronization between modules in large modular networks. Our work could help to understand the effects of localized regulatory actions on modular systems with synchronous phenomena, such as neuroscience and other fields
Analysis and Design of Adaptive Synchronization of a Complex Dynamical Network with Time-Delayed Nodes and Coupling Delays
This paper is devoted to the study of synchronization problems in uncertain dynamical networks with time-delayed nodes and coupling delays. First, a complex dynamical network model with time-delayed nodes and coupling delays is given. Second, for a complex dynamical network with known or unknown but bounded nonlinear couplings, an adaptive controller is designed, which can ensure that the state of a dynamical network asymptotically synchronizes at the individual node state locally or globally in an arbitrary specified network. Then, the Lyapunov-Krasovskii stability theory is employed to estimate the network coupling parameters. The main results provide sufficient conditions for synchronization under local or global circumstances, respectively. Finally, two typical examples are given, using the M-G system as the nodes of the ring dynamical network and second-order nodes in the dynamical network with time-varying communication delays and switching communication topologies, which illustrate the effectiveness of the proposed controller design methods
Synchronization in a Novel Local-World Dynamical Network Model
Advances in complex network research have recently stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. In the paper, we study the synchronizability of a class of local-world dynamical networks. Then, we have proposed a local-world synchronization-optimal growth topology model. Compared with the local-world evolving network model, it exhibits a stronger synchronizability. We also investigate the robustness of the synchronizability with respect to random failures and the fragility of the synchronizability with specific removal of nodes
Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons
Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data
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