- Published on 22 December 2021
Complex networks, which consist of many interacting dynamical systems, can represent a variety of emerging behaviors. There are lots of frameworks for modeling complex networks ranging from single-layer to multi-layer structures. A multi-layer network is efficient when there are different levels or types of connectivity. One of the essential collective behaviors in complex networks is synchronization which is observed commonly in nature. In this phenomenon, the dynamics of the coupled systems evolve, and eventually lead to a common motion. Various types of synchronization can be developed in a network, such as phase, amplitude, and lag synchronization. Besides, in exceptional cases, partial synchronization appears among oscillators. The chimera state is an example of partial synchronizations formed by the coexistence of the synchronous and asynchronous states. These collective behaviors can be found in numerous sciences, ranging from physical to biological networks, including neural networks. Synchronization of the neurons has a vital role in the functioning or malfunctioning of the brain. In many natural neuronal processes, such as some brain disorders, e.g., schizophrenia or epileptic seizures, evidence of chimera has been reported.
Various statistical measures have been proposed to evaluate collective behaviors. However, applying these measures depends on the properties of the emerging dynamics. The most widely used ones are the global order parameter, the local order parameter, the strength of incoherence, etc. Furthermore, one of the applicable methods for investigating synchronization is the Master Stability Function (MSF). Many scientists have focused on the generalization of the MSF to different conditions. The other important point in synchronization is how the network transits from asynchronization to synchronization. Generally, a network can move from an incoherent state to a coherent one by increasing the coupling coefficient. If this transition occurs gradually, it is called the second-order transition. In contrast, a sudden change happens in the first-order transition, which is termed explosive synchronization. Explosive synchronization has been a hot topic in recent years. The type of synchronization transition has been studied in various oscillators and networks. The critical slowing down in a complex network is another interesting field of study. The bifurcations of complex networks can be discussed from multiple viewpoints based on their applications.
This special issue will review the current state of the art about the networks of oscillators, their dynamics, and their applications in biological modeling and point out the directions of further studies. Papers investigating these topics are highly welcome.
Call for papers: The guest editors would like to cordially invite further authors to submit their original research papers for this special issue along the lines described above. An extended description of the critical aspects/open problems of the methods presented will be a stringent criterion of pre-selection of papers to be sent to referees. Articles may be one of four types: (i) minireviews (10-15 pages), (ii) tutorial reviews (15+ pages), (iii) original paper v1 (5-10 pages), or (iv) original paper v2 (3-5 pages). More detailed descriptions of each paper type can be found in the Authors’ Instructions. Manuscripts should be prepared using the latex template (preferably 2-column layout), which can be downloaded here.
Articles should be submitted to the Editorial Office of EPJ ST via the submission system, and should be clearly identified as intended for the topical issue “Collective behavior of nonlinear dynamical oscillators”.
Lead Guest Editor
Open Access: EPJST is a hybrid journal offering Open Access publication via the Open Choice programme and a growing number of Springer Compact “Publish and Read” arrangements which enable authors to publish OA at no direct cost (all costs are paid centrally).