Control for a synchronization-desynchronization switch

Controlling collective synchrony in oscillatory ensembles by precisely timed pulses

We present an efficient technique for control of synchrony in a globally coupled ensemble by pulsatile action. We assume that we can observe the collective oscillation and can stimulate all elements of the ensemble simultaneously. We pay special attention to the minimization of intervention into the system. The key idea is to stimulate only at the most sensitive phase. To find this phase, we implement an adaptive feedback control. Estimating the instantaneous phase of the collective mode on the fly, we achieve efficient suppression using a few pulses per oscillatory cycle. We discuss the possible relevance of the results for neuroscience, namely, for the development of advanced algorithms for deep brain stimulation, a medical technique used to treat Parkinson's disease.

Control of brain network dynamics across diverse scales of space and time

The human brain is composed of distinct regions that are each associated with particular functions and distinct propensities for the control of neural dynamics. However, the relation between these functions and control profiles is poorly understood, as is the variation in this relation across diverse scales of space and time. Here we probe the relation between control and dynamics in brain networks constructed from diffusion tensor imaging data in a large community sample of young adults. Specifically, we probe the control properties of each brain region and investigate their relationship with dynamics across various spatial scales using the Laplacian eigenspectrum. In addition, through analysis of regional modal controllability and partitioning of modes, we determine whether the associated dynamics are fast or slow, as well as whether they are alternating or monotone. We find that brain regions that facilitate the control of energetically easy transitions are associated with activity on short length scales and slow timescales. Conversely, brain regions that facilitate control of difficult transitions are associated with activity on long length scales and fast timescales. Built on linear dynamical models, our results offer parsimonious explanations for the activity propagation and network control profiles supported by regions of differing neuroanatomical structure.

Enhancing network synchronizability by strengthening a single node

In improving the stability of complex dynamical systems, an outstanding problem is how to achieve the desired performance at a low cost. For engineering and biological complex systems whose performance and functionality rely on the synchronous motion of their units, an important question related to the performance-cost-balance problem is how to improve efficiently the system synchronizability when a small amount of additional coupling resource is available. Here, employing a complex network of coupled chaotic oscillators as the model, we address this question by introducing a small amount of coupling intensity to only a single oscillator and investigate how the improvement of the network synchronizability is dependent on the location of the target oscillator. Theoretical analysis shows that, to achieve the maximum network synchronizability, the target oscillator to be strengthened should be chosen according to the eigenvector of the most unstable mode. Based on the theoretical finding, we further propose a single-node-based scheme for improving synchronization: the eigenvector-centrality-based strengthening scheme. We describe in detail how to apply this scheme under different synchronization scenarios and justify its efficiency in various network models by numerical simulations. The performance of the new scheme is compared with the conventional ones based on betweenness, closeness, and degree centralities, and it is shown that the new scheme has a clear advantage over the conventional ones. Furthermore, by a brute-force search of the target oscillator over the network, it is verified numerically that the oscillator identified by the new scheme indeed gives the best synchronization performance.

Perturbation analysis and comparison of network synchronization methods

In many networked systems, synchronization is important and useful, and how to enhance synchronizability is an interesting problem. Based on the matrix perturbation theory, we analyze five methods of network synchronization enhancement, including the link removal, node removal, dividing hub node, pull control, and pinning control methods, and obtain explicit expressions for eigenvalue changes. By these comparisons, we find that, among all these methods, the pull control method is remarkable, as it can extend the synchronization (coupling strength) region from both the left and right sides, for any controlled node. Extensive simulation results are given to support the accuracy of the perturbation-based analysis.

Subgraphs of functional brain networks identify dynamical constraints of cognitive control

Brain anatomy and physiology support the human ability to navigate a complex space of perceptions and actions. To maneuver across an ever-changing landscape of mental states, the brain invokes cognitive control-a set of dynamic processes that engage and disengage different groups of brain regions to modulate attention, switch between tasks, and inhibit prepotent responses. Current theory posits that correlated and anticorrelated brain activity may signify cooperative and competitive interactions between brain areas that subserve adaptive behavior. In this study, we use a quantitative approach to identify distinct topological motifs of functional interactions and examine how their expression relates to cognitive control processes and behavior. In particular, we acquire fMRI BOLD signal in twenty-eight healthy subjects as they perform two cognitive control tasks-a Stroop interference task and a local-global perception switching task using Navon figures-each with low and high cognitive control demand conditions. Based on these data, we construct dynamic functional brain networks and use a parts-based, network decomposition technique called non-negative matrix factorization to identify putative cognitive control subgraphs whose temporal expression captures distributed network structures involved in different phases of cooperative and competitive control processes. Our results demonstrate that temporal expression of the subgraphs fluctuate alongside changes in cognitive demand and are associated with individual differences in task performance. These findings offer insight into how coordinated changes in the cooperative and competitive roles of cognitive systems map trajectories between cognitively demanding brain states.

How to desynchronize quorum-sensing networks

In this paper we investigate how so-called quorum-sensing networks can be desynchronized. Such networks, which arise in many important application fields, such as systems biology, are characterized by the fact that direct communication between network nodes is superimposed to communication with a shared, environmental variable. In particular, we provide a new sufficient condition ensuring that the trajectories of these quorum-sensing networks diverge from their synchronous evolution. Then, we apply our result to study two applications.

A network engineering perspective on probing and perturbing cognition with neurofeedback

Network science and engineering provide a flexible and generalizable tool set to describe and manipulate complex systems characterized by heterogeneous interaction patterns among component parts. While classically applied to social systems, these tools have recently proven to be particularly useful in the study of the brain. In this review, we describe the nascent use of these tools to understand human cognition, and we discuss their utility in informing the meaningful and predictable perturbation of cognition in combination with the emerging capabilities of neurofeedback. To blend these disparate strands of research, we build on emerging conceptualizations of how the brain functions (as a complex network) and how we can develop and target interventions or modulations (as a form of network control). We close with an outline of current frontiers that bridge neurofeedback, connectomics, and network control theory to better understand human cognition.

Virtual Cortical Resection Reveals Push-Pull Network Control Preceding Seizure Evolution

In ∼20 million people with drug-resistant epilepsy, focal seizures originating in dysfunctional brain networks will often evolve and spread to surrounding tissue, disrupting function in otherwise normal brain regions. To identify network control mechanisms that regulate seizure spread, we developed a novel tool for pinpointing brain regions that facilitate synchronization in the epileptic network. Our method measures the impact of virtually resecting putative control regions on synchronization in a validated model of the human epileptic network. By applying our technique to time-varying functional networks, we identified brain regions whose topological role is to synchronize or desynchronize the epileptic network. Our results suggest that greater antagonistic push-pull interaction between synchronizing and desynchronizing brain regions better constrains seizure spread. These methods, while applied here to epilepsy, are generalizable to other brain networks and have wide applicability in isolating and mapping functional drivers of brain dynamics in health and disease.

Effective centrality and explosive synchronization in complex networks

Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. We here propose an effective network whose topological properties reflect the interplay between the topology and dynamics of the original network. On that basis, we are able to introduce the effective centrality, a measure that quantifies the role and importance of each network's node in the synchronization process. In particular, in the context of explosive synchronization, we use such a measure to assess the propensity of a graph to sustain an irreversible transition to synchronization. We furthermore discuss a strategy to induce the explosive behavior in a generic network, by acting only upon a fraction of its nodes.

Experimental Study of the Triplet Synchronization of Coupled Nonidentical Mechanical Metronomes

Triplet synchrony is an interesting state when the phases and the frequencies of three coupled oscillators fulfill the conditions of a triplet locking, whereas every pair of systems remains asynchronous. Experimental observation of triplet synchrony is firstly realized in three coupled nonidentical mechanical metronomes. A more direct method based on the phase diagram is proposed to observe and determine triplet synchronization. Our results show that the stable triplet synchrony is observed in several intervals of the parameter space. Moreover, the experimental results are verified according to the theoretical model of the coupled metronomes. The outcomes are useful to understand the inner regimes of collective dynamics in coupled oscillators.