Random temporal connections promote network synchronization

Collective synchronization through noise cancellation

After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: Deterministic coupling and common forcing. The inclusion of independent noise in these models typically serves to drive disorder, increasing the stability of the incoherent state. Here we show that the reverse is also possible. We propose and analyze a simple general model of purely noise coupled oscillators. In the first explicit choice of noise coupling, we find the linear response around incoherence is identical to that of the paradigmatic Kuramoto model but exhibits binary phase locking instead of full coherence. We characterize the phase diagram, stationary states, and approximate low-dimensional dynamics for the model, revealing the curious behavior of this mechanism of synchronization. In the second minimal case we connect the final synchronized state to the initial conditions of the system.

Desynchronizing oscillators coupled in multi-cluster networks through adaptively controlling partial networks

This article introduces an adaptive control scheme with a feedback delay, specifically designed for controlling partial networks, to achieve desynchronization in a coupled network with two or multiple clusters. The proposed scheme's effectiveness is validated through several representative examples of coupled neuronal networks with two interconnected clusters. The efficacy of this scheme is attributed to the rigorous and numerical analyses on the corresponding transcendental characteristic equation, which includes time delay and other network parameters. In addition to investigating the impact of time delay and inter-connectivity on the stability of an incoherent state, we also rigorously find that controlling only one cluster cannot realize the desynchronization in the coupled oscillators within three or more clusters. All these, we believe, can deepen the understanding of the deep brain stimulation techniques presently used in the clinical treatment of neurodegenerative diseases and suggest future avenues for enhancing these clinical techniques through adaptive feedback settings.

Complex Dynamics of Noise-Perturbed Excitatory-Inhibitory Neural Networks With Intra-Correlative and Inter-Independent Connections

Real neural system usually contains two types of neurons, i.e., excitatory neurons and inhibitory ones. Analytical and numerical interpretation of dynamics induced by different types of interactions among the neurons of two types is beneficial to understanding those physiological functions of the brain. Here, we articulate a model of noise-perturbed random neural networks containing both excitatory and inhibitory (E&I) populations. Particularly, both intra-correlatively and inter-independently connected neurons in two populations are taken into account, which is different from the most existing E&I models only considering the independently-connected neurons. By employing the typical mean-field theory, we obtain an equivalent system of two dimensions with an input of stationary Gaussian process. Investigating the stationary autocorrelation functions along the obtained system, we analytically find the parameters’ conditions under which the synchronized behaviors between the two populations are sufficiently emergent. Taking the maximal Lyapunov exponent as an index, we also find different critical values of the coupling strength coefficients for the chaotic excitatory neurons and for the chaotic inhibitory ones. Interestingly, we reveal that the noise is able to suppress chaotic dynamics of the random neural networks having neurons in two populations, while an appropriate amount of correlation coefficient in intra-coupling strengths can enhance chaos occurrence. Finally, we also detect a previously-reported phenomenon where the parameters region corresponds to neither linearly stable nor chaotic dynamics; however, the size of the region area crucially depends on the populations’ parameters.

Edges of inter-layer synchronization in multilayer networks with time-switching links

We investigate the transition to synchronization in a two-layer network of oscillators with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the timescale of topological changes. Initially, we observe a smooth transition to complete synchronization for the static inter-layer topology by increasing the number of inter-layer links. Next, for a dynamic topology with the existent inter-layer links randomly changing among identical oscillators in the layers, we observe a significant improvement in the system synchronizability; i.e., the layers synchronize with lower inter-layer connectivity. More interestingly, we find that, for a critical switching time, the transition from the network state of low inter-layer synchronization to high inter-layer synchronization occurs abruptly as the number of inter-layer links increases. We interpret this phenomenon as shrinking and ultimately the disappearance of the basin of attraction of a desynchronized network state.

Designing temporal networks that synchronize under resource constraints

Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources. Such resource constraints are often reflected as a finite coupling budget available in a network to facilitate interaction and communication. Here, we show that introducing temporal variation in the network structure can lead to efficient synchronization even when stable synchrony is impossible in any static network under the given budget, thereby demonstrating a fundamental advantage of temporal networks. The temporal networks generated by our open-loop design are versatile in the sense of promoting synchronization for systems with vastly different dynamics, including periodic and chaotic dynamics in both discrete-time and continuous-time models. Furthermore, we link the dynamic stabilization effect of the changing topology to the curvature of the master stability function, which provides analytical insights into synchronization on temporal networks in general. In particular, our results shed light on the effect of network switching rate and explain why certain temporal networks synchronize only for intermediate switching rate.

The ability of complex networks to synchronize themselves is limited by available coupling resources. Zhang and Strogatz show that allowing temporal variation in the network structure can lead to synchronization even when stable synchrony is impossible in any static network under the fixed budget.

A theory of pattern formation for reaction–diffusion systems on temporal networks

Networks have become ubiquitous in the modern scientific literature, with recent work directed at understanding ‘temporal networks’—those networks having structure or topology which evolves over time. One area of active interest is pattern formation from reaction–diffusion systems, which themselves evolve over temporal networks. We derive analytical conditions for the onset of diffusive spatial and spatio-temporal pattern formation on undirected temporal networks through the Turing and Benjamin–Feir mechanisms, with the resulting pattern selection process depending strongly on the evolution of both global diffusion rates and the local structure of the underlying network. Both instability criteria are then extended to the case where the reaction–diffusion system is non-autonomous, which allows us to study pattern formation from time-varying base states. The theory we present is illustrated through a variety of numerical simulations which highlight the role of the time evolution of network topology, diffusion mechanisms and non-autonomous reaction kinetics on pattern formation or suppression. A fundamental finding is that Turing and Benjamin–Feir instabilities are generically transient rather than eternal, with dynamics on temporal networks able to transition between distinct patterns or spatio-temporal states. One may exploit this feature to generate new patterns, or even suppress undesirable patterns, over a given time interval.

Cross-sectional focusing of red blood cells in a constricted microfluidic channel

Constrictions in blood vessels and microfluidic devices can dramatically change the spatial distribution of passing cells or particles and are commonly used in biomedical cell sorting applications. However, the three-dimensional nature of cell focusing in the channel cross-section remains poorly investigated. Here, we explore the cross-sectional distribution of living and rigid red blood cells passing a constricted microfluidic channel by tracking individual cells in multiple layers across the channel depth and across the channel width. While cells are homogeneously distributed in the channel cross-section pre-contraction, we observe a strong geometry-induced focusing towards the four channel faces post-contraction. The magnitude of this cross-sectional focusing effect increases with increasing Reynolds number for both living and rigid red blood cells. We discuss how this non-uniform cell distribution downstream of the contraction results in an apparent double-peaked velocity profile in particle image velocimetry analysis and show that trapping of red blood cells in the recirculation zones of the abrupt construction depends on cell deformability.