Abstract
With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.
Original language | English |
---|---|
Article number | 034313 |
Journal | Physical Review E |
Volume | 107 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2023 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2023 American Physical Society.
Funding
We greatly appreciate the insightful comments provided by anonymous referees that helped greatly improve the manuscript. S.N.C. wants to convey his sincere gratitude to Md Sayeed Anwar of the Indian Statistical Institute for several valuable discussions. In fact, all authors are in debt to Md Sayeed Anwar for helpful comments on the manuscript. S.N.C. also wants to thank the Department of Science and Technology, Govt. of India, for the financial support through Grant No. NMICPS/006/MD/2020-21 during the end of this work. C.H. is supported by DST-INSPIRE Faculty Grant No. IFA17-PH193.
Funders | Funder number |
---|---|
Department of Science and Technology, Ministry of Science and Technology, India | IFA17-PH193 |