Abstract
A series of recent publications, within the framework of network science, have focused on the coexistence of mixed attractive and repulsive (excitatory and inhibitory) interactions among the units within the same system, motivated by the analogies with spin glasses as well as to neural networks, or ecological systems. However, most of these investigations have been restricted to single layer networks, requiring further analysis of the complex dynamics and particular equilibrium states that emerge in multilayer configurations. This article investigates the synchronization properties of dynamical systems connected through multiplex architectures in the presence of attractive intralayer and repulsive interlayer connections. This setting enables the emergence of antisynchronization, i.e., intralayer synchronization coexisting with antiphase dynamics between coupled systems of different layers. We demonstrate the existence of a transition from interlayer antisynchronization to antiphase synchrony in any connected bipartite multiplex architecture when the repulsive coupling is introduced through any spanning tree of a single layer. We identify, analytically, the required graph topologies for interlayer antisynchronization and its interplay with intralayer and antiphase synchronization. Next, we analytically derive the invariance of intralayer synchronization manifold and calculate the attractor size of each oscillator exhibiting interlayer antisynchronization together with intralayer synchronization. The necessary conditions for the existence of interlayer antisynchronization along with intralayer synchronization are given and numerically validated by considering Stuart-Landau oscillators. Finally, we also analytically derive the local stability condition of the interlayer antisynchronization state using the master stability function approach.
Original language | English |
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Article number | 032310 |
Journal | Physical Review E |
Volume | 103 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2021 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2021 American Physical Society.
Funding
S.N.C. and D.G. were supported by Department of Science and Technology, Government of India (Project No. EMR/2016/001039). S.N.C. would also like to thank Physics and Applied Mathematics Unit of Indian Statistical Institute, Kolkata, for their financial support. S.N.C would also like to acknowledge the financial support from the CSIR [Project No. 09/093(0194)/2020-EMR-I] for funding him during the end part of this work. J.M.B. is funded by MINECO (Project No. FIS2017-84151-P). C.H. is supported by DST-INSPIRE Faculty Grant No. IFA17-PH193.
Funders | Funder number |
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DST-INSPIRE | IFA17-PH193 |
Department of Science and Technology, Ministry of Science and Technology, India | EMR/2016/001039 |
Council of Scientific and Industrial Research, India | 09/093(0194)/2020-EMR-I |
Ministerio de Economía y Competitividad | FIS2017-84151-P |