Thanh bên bài viết

PDF
Ngày xuất bản: 10/10/2021
Ngày xuất bản Online: 10/10/2021
Số lượt xem tóm tắt: 70
Số lượt xem PDF: 61
DOI: https://doi.org/10.52714/dthu.10.5.2021.889
Số xuất bản
Tập 10 Số 5 (2021): Chuyên san Khoa học Tự nhiên (Tiếng Anh)
Chuyên mục
Khoa học Tự nhiên (Tiếng Anh)
Trích dẫn bài báo
Phan, V. L. E. (2021). Synchronization in complete networks of ordinary differential equations of Fitzhugh – Nagumo type with nonlinear coupling. Tạp chí Khoa học Đại học Đồng Tháp, 10(5), 3-9. https://doi.org/10.52714/dthu.10.5.2021.889

Synchronization in complete networks of ordinary differential equations of Fitzhugh – Nagumo type with nonlinear coupling

Phan Van Long Em1,
1 An Giang University, Vietnam National University Ho Chi Minh City, Vietnam

Nội dung chính của bài viết

Tóm tắt

Synchronization is a ubiquitous feature in many natural systems and nonlinear science. This paper studies the synchronization in a complete network consisting of n nodes. Each node is connected to all other nodes by nonlinear coupling and represented by an ordinary differential system of FitzHugh-Nagumo type (FHN) which can be obtained by simplifying the famous Hodgkin-Huxley model. From this complete network, a sufficient condition on the coupling strength is identified to achieve the synchronization. The result shows that the networks with bigger in-degrees of the nodes synchronize more easily. The paper also shows this theoretical result numerically and see that there is a compromise.

Chi tiết bài viết

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Từ khóa

Coupling strength, complete network, FitzHugh-Nagumo model, nonlinear coupling, synchronization

Tài liệu tham khảo

Ambrosio, B. (2009). Propagation d'ondes dans un milieu excitable: simulations numériques et approche analytique. Thesis, University Pierre and Marie Curie- Paris 6, France.
Ambrosio, B., & Aziz-Alaoui, M. A. (2012). Synchronization and control of coupled reaction-diffusion systems of the FitzHugh-Nagumo-type. Computers and Mathematics with Application, (64), 934-943.
Ambrosio, B., & Aziz-Alaoui, M. A. (2013). Synchronization and control of a network of coupled reaction-diffusion systems of generalized FitzHugh-Nagumo type. ESAIM: Proceedings, (39), 15-24.
Aziz-Alaoui, M. A. (2006). Synchronization of Chaos. Encyclopedia of Mathematical Physics, Elsevier, (5), 213-226.
Ambrosio, B., Aziz-Alaoui, M. A., & Phan, V. L. E. (2018). Global attractor of complex networks of reaction-diffusion systems of Fitzhugh-Nagumo type. Discrete and continuous dynamical systems series B, (23), 3787-3797.
Belykh, I., De Lange, E., & Hasler, M. (2005). Synchronization of bursting neurons: What matters in the network topology. Phys. Rev. Lett., (94), 188101.
Corson, N. (2009). Dynamique d'un modèle neuronal, synchronisation et complexité. Thesis, University of Le Havre, France.
Ermentrout, G. B., & Terman, D. H. (2009). Mathematical foundations of neurosciences, Interdisciplinary Applied Mathematics, Springer.
Fitzhugh, R. (1960). Thresholds and plateaus in the Hodgkin–Huxley nerve equations. J. Gen. Physiol., (43), 867-896.
Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and ts application to conduction and excitation in nerve. J. Physiol., (117), 500-544.
Izhikevich, E. M. (2007). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. Computational Neuroscience Series, Poggio The MIT Press, Cambridge.
Keener, J. P., & Sneyd, J. (2009). Mathematical Physiology: Systems Physiology, Second Edition. Antman S.S., Marsden J.E., and Sirovich L. Springer.
Murray, J. D. (2002). Mathematical Biology. I. An Introduction, Third Edition. Springer.
Nagumo, J., Arimoto, S., & Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon. Proc. IRE., (50), 2061-2070.
Pikovsky, A., Rosenblum, M., & Kurths, J. (2001). Synchronization, A Universal Concept in Nonlinear Science. Cambridge: Cambridge University Press.