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The European Physical Journal Special Topics

, Volume 228, Issue 11, pp 2371–2379 | Cite as

Spiral wave in a two-layer neuronal network

  • Yu Feng
  • Abdul Jalil M. Khalaf
  • Fawaz E. Alsaadi
  • Tasawar Hayat
  • Viet-Thanh PhamEmail author
Regular Article
Part of the following topical collections:
  1. Diffusion Dynamics and Information Spreading in Multilayer Networks

Abstract

Multi-layer networks are quite fundamental to study structural and functional properties of various biological systems. In this study, a two-layer neuronal network is considered and the interactions between the spiral pattern in one layer and a homogeneous state in the other layer, under the effect of inter-layer bidirectional connection are investigated. Spiral wave has been confirmed to play a significant role in many complex systems. In this regard, in laminar structured systems in particular, it is crucial to study the dynamics of the spiral wave affected by the inter-layer interactions. Here, for each layer (sub-network), a regular network with eight-neighbor connection is designed. For the local dynamics of each neuron, the magnetic Fitzhugh–Nagumo (FN) neuronal model is introduced. The results show that depending on the level of interactions between the two layers, four different types of collective electrical activity can occur. When the inter-layer connection is weak, the layer with spiral pattern does not change while the homogeneous state of the other layer is broken by a blurred spiral pattern. As the inter-layer connection is strengthened, the dynamics of the spiral wave changes significantly, leading to unstable spiral wave and spiral turbulence. However, by a further increase in the inter-layer coupling strength, the spiral wave does not exist at all.

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Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yu Feng
    • 1
  • Abdul Jalil M. Khalaf
    • 2
  • Fawaz E. Alsaadi
    • 3
  • Tasawar Hayat
    • 4
    • 5
  • Viet-Thanh Pham
    • 6
    Email author
  1. 1.Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal UniversityYulin, GuangxiP.R. China
  2. 2.Ministry of Higher Education and Scientific ResearchBaghdadIraq
  3. 3.Department of Information TechnologyFaculty of Computing and IT, King Abdulaziz UniversityJeddahSaudi Arabia
  4. 4.Department of MathematicsQuaid-I-Azam University 45320IslamabadPakistan
  5. 5.NAAM Research Group, King Abdulaziz UniversityJeddahSaudi Arabia
  6. 6.Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang UniversityHo Chi Minh CityVietnam

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