Enhancing network synchronization by phase modulation

Optimal time-varying coupling function can enhance synchronization in complex networks

In this paper, we propose a time-varying coupling function that results in enhanced synchronization in complex networks of oscillators. The stability of synchronization can be analyzed by applying the master stability approach, which considers the largest Lyapunov exponent of the linearized variational equations as a function of the network eigenvalues as the master stability function. Here, it is assumed that the oscillators have diffusive single-variable coupling. All possible single-variable couplings are studied for each time interval, and the one with the smallest local Lyapunov exponent is selected. The obtained coupling function leads to a decrease in the critical coupling parameter, resulting in enhanced synchronization. Moreover, synchronization is achieved faster, and its robustness is increased. For illustration, the optimum coupling function is found for three networks of chaotic Rössler, Chen, and Chua systems, revealing enhanced synchronization.

Inferring synchronizability of networked heterogeneous oscillators with machine learning

In the study of network synchronization, an outstanding question of both theoretical and practical significance is how to allocate a given set of heterogeneous oscillators on a complex network in order to improve the synchronization performance. Whereas methods have been proposed to address this question in the literature, the methods are all based on accurate models describing the system dynamics, which, however, are normally unavailable in realistic situations. Here, we show that this question can be addressed by the model-free technique of a feed-forward neural network (FNN) in machine learning. Specifically, we measure the synchronization performance of a number of allocation schemes and use the measured data to train a machine. It is found that the trained machine is able to not only infer the synchronization performance of any new allocation scheme, but also find from a huge amount of candidates the optimal allocation scheme for synchronization.

Effects of topological characteristics on rhythmic states of the D-dimensional Kuramoto model in complex networks

Synchronization is a ubiquitous phenomenon in engineering and natural ecosystems. While the dynamics of synchronization modeled by the Kuramoto model are commonly studied in two dimensions and the state of dynamic units is characterized by a scalar angle variable, we studied the Kuramoto model generalized to D dimensions in the framework of a complex network and utilized the local synchronous order parameter between the agent and its neighbors as the controllable variable to adjust the coupling strength. Here, we reported that average connectivity of networks affects the time-dependent, rhythmic, cyclic state. Importantly, we found that the level of heterogeneity of networks governs the rhythmic state in the transition process. The analytical treatment for observed scenarios in a D-dimensional Kuramoto model at D=3 was provided. These results offered a platform for a better understanding of time-dependent swarming and flocking dynamics in nature.

The Continuum Between Temperament and Mental Illness as Dynamical Phases and Transitions

The full range of biopsychosocial complexity is mind-boggling, spanning a vast range of spatiotemporal scales with complicated vertical, horizontal, and diagonal feedback interactions between contributing systems. It is unlikely that such complexity can be dealt with by a single model. One approach is to focus on a narrower range of phenomena which involve fewer systems but still cover the range of spatiotemporal scales. The suggestion is to focus on the relationship between temperament in healthy individuals and mental illness, which have been conjectured to lie along a continuum of neurobehavioral regulation involving neurochemical regulatory systems (e.g., monoamine and acetylcholine, opiate receptors, neuropeptides, oxytocin), and cortical regulatory systems (e.g., prefrontal, limbic). Temperament and mental illness are quintessentially dynamical phenomena, and need to be addressed in dynamical terms. A meteorological metaphor suggests similarities between temperament and chronic mental illness and climate, between individual behaviors and weather, and acute mental illness and frontal weather events. The transition from normative temperament to chronic mental illness is analogous to climate change. This leads to the conjecture that temperament and chronic mental illness describe distinct, high level, dynamical phases. This suggests approaching biopsychosocial complexity through the study of dynamical phases, their order and control parameters, and their phase transitions. Unlike transitions in physical systems, these biopsychosocial phase transitions involve information and semiotics. The application of complex adaptive dynamical systems theory has led to a host of markers including geometrical markers (periodicity, intermittency, recurrence, chaos) and analytical markers such as fluctuation spectroscopy, scaling, entropy, recurrence time. Clinically accessible biomarkers, in particular heart rate variability and activity markers have been suggested to distinguish these dynamical phases and to signal the presence of transitional states. A particular formal model of these dynamical phases will be presented based upon the process algebra, which has been used to model information flow in complex systems. In particular it describes the dual influences of energy and information on the dynamics of complex systems. The process algebra model is well-suited for dealing with the particular dynamical features of the continuum, which include transience, contextuality, and emergence. These dynamical phases will be described using the process algebra model and implications for clinical practice will be discussed.

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.