Global Synchronization Of Network Research Articles

Effect of hidden geometry and higher-order interactions on the synchronization and hysteresis behavior of phase oscillators on 5-clique simplicial assemblies.

The hidden geometry of simplicial complexes can influence the collective dynamics of nodes in different ways depending on the simplex-based interactions of various orders and competition between local and global structural features. We study a system of phase oscillators attached to nodes of four-dimensional simplicial complexes and interacting via positive/negative edges-based pairwise K_{1} and triangle-based triple K_{2}≥0 couplings. Three prototypal simplicial complexes are grown by aggregation of 5-cliques, controlled by the chemical affinity parameter ν, resulting in sparse, mixed, and compact architecture, all of which have 1-hyperbolic graphs but different spectral dimensions. By changing the interaction strength K_{1}∈[-4,2] along the forward and backward sweeps, we numerically determine individual phases of each oscillator and a global order parameter to measure the level of synchronization. Our results reveal how different architectures of simplicial complexes, in conjunction with the interactions and internal-frequency distributions, impact the shape of the hysteresis loop and lead to patterns of locally synchronized groups that hinder global network synchronization. Remarkably, these groups are differently affected by the size of the shared faces between neighboring 5-cliques and the presence of higher-order interactions. At K_{1}<0, partial synchronization is much higher in the compact community than in the assemblies of cliques sharing single nodes, at least occasionally. These structures also partially desynchronize at a lower triangle-based coupling K_{2} than the compact assembly. Broadening of the internal frequency distribution gradually reduces the synchronization level in the mixed and sparse communities, even at positive pairwise couplings. The order-parameter fluctuations in these partially synchronized states are quasicyclical with higher harmonics, described by multifractal analysis and broad singularity spectra.

Evaluation of Frequency-Dependent Effects of Deep Brain Stimulation in a Cortex-Basal Ganglia-Thalamus Network Model of Parkinson's Disease.

Parkinson's disease (PD) is a chronic neurodegenerative disease whose motor symptoms are accompanied by an exaggerated power in the alpha-beta (7-35Hz) band and an increased synchronization of neurons encompassing the cortex-basal ganglia-thalamus network. Currently, deep brain stimulation (DBS) is used as an effective therapy for reducing the excessive power and synchrony observed in brain circuits, thereby ameliorating the PD symptoms. In the present study, we used a biologically plausible computational model of cortex-basal ganglia-thalamus network, which represents both healthy and PD conditions, to systematically investigate the effects of DBS frequency on the model outputs. DBS was applied to the subthalamic nucleus (STN) at different stimulation frequencies (40Hz to 300Hz). Spike train variability and spectral power in the 7-35Hz band were measured from the several nuclei represented in the model. In addition, the magnitude squared coherence between the nuclei was assessed. An increased DBS frequency tended to produce interspike intervals (ISIs) with higher variability as compared to PD condition. Also, DBS significantly reduced the alpha-beta power for almost all brain nuclei. The median of the magnitude-squared coherence matrix (which is a metric of global network synchronization) decreased significantly with the increase of DBS frequency.

Observer-based synchronization in fractional-order leader–follower complex networks

This paper is devoted to synchronization behavior of complex dynamical networks with a Caputo fractional-order derivative. In particular, we propose a fractional-order leader–follower complex network where the leader is independent, has its own dynamics, and is followed by all the other nodes. Using the state observer approach, the leader and the followers are designed to connect through only a scalar coupling signal instead of the commonly used full state coupling scheme. On the basis of stability theory of the fractional-order differential system, a sufficient condition for global network synchronization is presented, which only relates to the linear part of individual nodes and can be easily solved by the pole-placement design technique. The analytic results are complemented with numerical simulations for a network whose nodes are governed by the fractional-order Chua’s circuit.

Ketamine disrupts theta synchrony across the septotemporal axis of the CA1 region of hippocampus

The hippocampal theta signal reflects moment-to-moment variation in the synchrony of synaptic input to hippocampal neurons. Consistent with the topography of hippocampal afferents, the synchrony (coherence) of the theta signal varies across the septotemporal axis. Septotemporal variation in the theta signal can also be observed in relation to ongoing and past experience. Thus there is a systematic decrease in the relationship between locomotor speed and theta power across the septotemporal axis, septal hippocampus exhibiting the strongest relationship. Conversely, theta in temporal hippocampus decrements over repeated behavioral experience (running episodes), while theta in the septal hippocampus does not. Ketamine is an N-methyl-D-aspartate (NMDA) antagonist that can decrease theta power. The present study examined whether ketamine treatment could alter theta coherence across the long axis independent of changes in locomotor behavior. Rats were well trained to navigate a linear runway and outfitted with electrodes at different septotemporal positions within CA1. Locomotor behavior and theta coherence and power were examined after administration of 2.5 and 10 mg/kg ketamine. Ketamine (2.5 mg/kg) decreased theta coherence between distant CA1 electrode sites without altering running speed or theta power. Both doses of ketamine also blunted and reversed the decrement in theta power observed at midseptotemporal and temporal electrodes over repeated run sessions. The results demonstrate the sensitivity of global network synchronization to relatively low doses of ketamine and septotemporal differences in the influence of ketamine on hippocampal dynamics in relation to past experience.

Exponential Synchronization of Complex Delayed Dynamical Networks With Switching Topology

This paper studies the local and global exponential synchronization of a complex dynamical network with switching topology and time-varying coupling delays. By using stability theory of switched systems and the network topology, the synchronization of such a network under some special switching signals is investigated. Firstly, under the assumption that all subnetworks are self-synchronizing, a delay-dependent sufficient condition is given in terms of linear matrix inequalities, which guarantees the solvability of the local synchronization problem under an average dwell time scheme. Then this result is extended to the situation that not all subnetworks are self-synchronizing. For the latter case, in addition to average dwell time, an extra condition on the ratio of the total activation time of self-synchronizing and nonsynchronizing subnetworks is needed to achieve synchronization of the entire switched network. The global synchronization of a network whose isolate dynamics is of a particular form is also studied. Three different examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.

Extension of Pairwise Broadcast Clock Synchronization for Multicluster Sensor Networks

Time synchronization is crucial for wireless sensor networks (WSNs) in performing a number of fundamental operations such as data coordination, power management, security, and localization. The Pairwise Broadcast Synchronization (PBS) protocol was recently proposed to minimize the number of timing messages required for global network synchronization, which enables the design of highly energy-efficient WSNs. However, PBS requires all nodes in the network to lie within the communication ranges of two leader nodes, a condition which might not be available in some applications. This paper proposes an extension of PBS to the more general class of sensor networks. Based on the hierarchical structure of the network, an energy-efficient pair selection algorithm is proposed to select the best pairwise synchronization sequence to reduce the overall energy consumption. It is shown that in a multicluster networking environment, PBS requires a far less number of timing messages than other well-known synchronization protocols and incurs no loss in synchronization accuracy. Moreover, the proposed scheme presents significant energy savings for densely deployed WSNs.

Topological design and dimensioning of Agile All-Photonic Networks

We present the design and analysis of an Agile All-Photonic Network (AAPN); in the context of our study, the agility is derived from sub-microsecond photonic switching and global network synchronization. We have articulated a set of circuit design alternatives in terms of switch configurations referred to as symmetric and asymmetric designs, and two-layer and three-layer designs and discuss the implications of these alternatives in terms of transmitter and receiver design and synchronization requirements. In order to evaluate performance and cost of this range of design alternatives, we developed a set of software tools and methodologies for designing and dimensioning our vision of an AAPN. The topological design problem consists of determining the optimal number, size and placement of edge nodes, selector/multiplexers and core switches as well as the placement of the DWDM links so as to minimize network costs while satisfying performance requirements of the supported traffic. A new mixed integer linear programming formulation is presented for core node placement and link connectivity. A methodology has been developed for two-layer and three-layer network topology design and implemented in software. These tools were exercised under a wide variety of equipment cost assumptions for both a metropolitan network and a long-haul network assuming a gravity model for traffic distribution and a flat community of interest factor. Key findings include the determination of near cost optimal designs for both metropolitan (two-layer design) and a Canadian wide area network (WAN, three-layer design). We also show the cost and topology sensitivity to the selector switch size and the preferred size in terms of port count and number of switches.