Amplification of explosive width in complex networks

Impact of phase lag on synchronization in frustrated Kuramoto model with higher-order interactions

The study of first order transition (explosive synchronization) in an ensemble (network) of coupled oscillators has been the topic of paramount interest among the researchers for more than one decade. Several frameworks have been proposed to induce explosive synchronization in a network and it has been reported that phase frustration in a network usually suppresses first order transition in the presence of pairwise interactions among the oscillators. However, on the contrary, by considering networks of phase frustrated coupled oscillators in the presence of higher-order interactions (up to 2-simplexes) we show here, under certain conditions, phase frustration can promote explosive synchronization in a network. A low-dimensional model of the network in the thermodynamic limit is derived using the Ott-Antonsen ansatz to explain this surprising result. Analytical treatment of the low-dimensional model, including bifurcation analysis, explains the apparent counter intuitive result quite clearly.

Perfect synchronization in complex networks with higher-order interactions

Achieving perfect synchronization in a complex network, specially in the presence of higher-order interactions (HOIs) at a targeted point in the parameter space, is an interesting, yet challenging task. Here we present a theoretical framework to achieve the same under the paradigm of the Sakaguchi-Kuramoto (SK) model. We analytically derive a frequency set to achieve perfect synchrony at some desired point in a complex network of SK oscillators with higher-order interactions. Considering the SK model with HOIs on top of the scale-free, random, and small world networks, we perform extensive numerical simulations to verify the proposed theory. Numerical simulations show that the analytically derived frequency set not only provides stable perfect synchronization in the network at a desired point but also proves to be very effective in achieving a high level of synchronization around it compared to the other choices of frequency sets. The stability and the robustness of the perfect synchronization state of the system are determined using the low-dimensional reduction of the network and by introducing a Gaussian noise around the derived frequency set, respectively.

Explosive Synchronization-Based Brain Modulation Reduces Hypersensitivity in the Brain Network: A Computational Model Study

Fibromyalgia (FM) is a chronic pain condition that is characterized by hypersensitivity to multimodal sensory stimuli, widespread pain, and fatigue. We have previously proposed explosive synchronization (ES), a phenomenon wherein a small perturbation to a network can lead to an abrupt state transition, as a potential mechanism of the hypersensitive FM brain. Therefore, we hypothesized that converting a brain network from ES to general synchronization (GS) may reduce the hypersensitivity of FM brain. To find an effective brain network modulation to convert ES into GS, we constructed a large-scale brain network model near criticality (i.e., an optimally balanced state between order and disorders), which reflects brain dynamics in conscious wakefulness, and adjusted two parameters: local structural connectivity and signal randomness of target brain regions. The network sensitivity to global stimuli was compared between the brain networks before and after the modulation. We found that only increasing the local connectivity of hubs (nodes with intense connections) changes ES to GS, reducing the sensitivity, whereas other types of modulation such as decreasing local connectivity, increasing and decreasing signal randomness are not effective. This study would help to develop a network mechanism-based brain modulation method to reduce the hypersensitivity in FM.

Assortativity-induced explosive synchronization in a complex neuronal network

In this study, we consider a scale-free network of nonidentical Chialvo neurons, coupled through electrical synapses. For sufficiently strong coupling, the system undergoes a transition from completely out of phase synchronized to phase synchronized state. The principal focus of this study is to investigate the effect of the degree of assortativity over the synchronization transition process. It is observed that, depending on assortativity, bistability between two asymptotically stable states allows one to develop a hysteresis loop which transforms the phase transition from second order to first order. An expansion in the area of hysteresis loop is noticeable with increasing degree-degree correlation in the network. Our study also reveals that effective frequencies of nodes simultaneously go through a continuous or sudden transition to the synchronized state with the corresponding phases. Further, we examine the robustness of the results under the effect of network size and average degree, as well as diverse frequency setup. Finally, we investigate the dynamical mechanism in the process of generating explosive synchronization. We observe a significant impact of lower degree nodes behind such phenomena: in a positive assortative network the low degree nodes delay the synchronization transition.

Explosive synchronization in interlayer phase-shifted Kuramoto oscillators on multiplex networks

Different methods have been proposed in the past few years to incite explosive synchronization (ES) in Kuramoto phase oscillators. In this work, we show that the introduction of a phase shift α in interlayer coupling terms of a two-layer multiplex network of Kuramoto oscillators can also instigate ES in the layers. As α→π/2, ES emerges along with hysteresis. The width of hysteresis depends on the phase shift α, interlayer coupling strength, and natural frequency mismatch between mirror nodes. A mean-field analysis is performed to justify the numerical results. Similar to earlier works, the suppression of synchronization is accountable for the occurrence of ES. The robustness of ES against changes in network topology and natural frequency distribution is tested. Finally, taking a suggestion from the synchronized state of the multiplex networks, we extend the results to classical single networks where some specific links are assigned phase-shifted interactions.

Transition to synchronization in heterogeneous inhibitory neural networks with structured synapses

Inhibitory neurons form an extensive network involved in the development of different rhythms in the cerebral cortex. A transition from an incoherent state, where all inhibitory neurons fire unrelated to each other, to a synchronized or locked state, where all or most neurons define a tight firing pattern, is maybe the most salient process to analyze when considering neuronal rhythms. In this work, we analyzed whether different patterns of effective synaptic connectivity may support a first-order-like transition in this path to synchronization. Such an "explosive" phenomenon may be relevant in neural processes, as normal cognitive processing in different tasks and some neurological disorders manifest an increased power in many neuronal rhythms, supported by an extended concerted spiking activity and an abrupt change to this state. Furthermore, we built an adaptive mechanism that supports the generation of this kind of network, which rapidly creates the underlying structure based on the ongoing firing statistics.

Explosive synchronization in temporal networks: A comparative study

We present a comparative study on Explosive Synchronization (ES) in temporal networks consisting of phase oscillators. The temporal nature of the networks is modeled with two configurations: (1) oscillators are allowed to move in a closed two-dimensional box such that they couple with their neighbors and (2) oscillators are static and they randomly switch their coupling partners. Configuration (1) is further studied under two possible scenarios: in the first case, oscillators couple to fixed numbers of neighbors, while, in the other case, they couple to all oscillators lying in their circle of vision. Under these circumstances, we monitor the degrees of temporal networks, velocities, and radius of circle of vision of the oscillators and the probability of forming connections in order to study and compare the critical values of the coupling required to induce ES in the population of phase oscillators.