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Complexity in time-delay networks of multiple interacting neural groups

  • Received: 01 December 2020 Revised: 01 January 2021 Published: 15 March 2021
  • 70K50, 92B20, 34Kxx

  • Coupled networks are common in diverse real-world systems and the dynamical properties are crucial for their function and application. This paper focuses on the behaviors of a network consisting of mutually coupled neural groups and time-delayed interactions. These interacting groups can include different sets of nodes and topological architecture, respectively. The local and global stability of the system are analyzed and the stable regions and bifurcation curves in parameter planes are obtained. Different patterns of bifurcated solutions arising from trivial and non-trivial equilibrium points are given, such as the coexistence of non-trivial equilibrium points and periodic responses and multiple coexisting periodic orbits. The bifurcation diagrams are shown and plenty of complex dynamic phenomena are observed, such as multi-period oscillations and multiple coexisting attractors.

    Citation: Xiaochen Mao, Weijie Ding, Xiangyu Zhou, Song Wang, Xingyong Li. Complexity in time-delay networks of multiple interacting neural groups[J]. Electronic Research Archive, 2021, 29(5): 2973-2985. doi: 10.3934/era.2021022

    Related Papers:

  • Coupled networks are common in diverse real-world systems and the dynamical properties are crucial for their function and application. This paper focuses on the behaviors of a network consisting of mutually coupled neural groups and time-delayed interactions. These interacting groups can include different sets of nodes and topological architecture, respectively. The local and global stability of the system are analyzed and the stable regions and bifurcation curves in parameter planes are obtained. Different patterns of bifurcated solutions arising from trivial and non-trivial equilibrium points are given, such as the coexistence of non-trivial equilibrium points and periodic responses and multiple coexisting periodic orbits. The bifurcation diagrams are shown and plenty of complex dynamic phenomena are observed, such as multi-period oscillations and multiple coexisting attractors.



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    [1] F. Battiston, V. Nicosia, M. Chavez and V. Latora, Multilayer motif analysis of brain networks, Chaos, 27 (2017), 047404, 8 pp. doi: 10.1063/1.4979282
    [2] The structure and dynamics of multilayer networks. Phys. Rep. (2014) 544: 1-122.
    [3] Delayed coupling between two neural network loops. SIAM J. Appl. Math. (2004) 65: 316-335.
    [4] Improving control effects of absence seizures using single-pulse alternately resetting stimulation (SARS) of corticothalamic circuit. Appl. Math. Mech. (Eng. Edit.) (2020) 41: 1287-1302.
    [5] F. Frohlich and M. Bazhenov, Coexistence of tonic firing and bursting in cortical neurons, Phys. Rev. E, 74 (2006), 031922.
    [6] Robust synchronization of bursting Hodgkin-Huxley neuronal systems coupled by delayed chemical synapses. Int. J. Nonlinear Mech. (2015) 70: 105-111.
    [7] Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Nati. Acad. Sci. USA (1984) 81: 3088-3092.
    [8] Periodic oscillations arising and death in delay-coupled neural loops. Internat. J. Bifur. Chaos Appl. Sci. Engrg. (2007) 17: 4015-4032.
    [9] H. Y. Hu and Z. H. Wang, Dynamics of Controlled Mechanical Systems with Delayed Feedback, Springer-Verlag, Heidelberg, 2002. doi: 10.1007/978-3-662-05030-9
    [10] S. Majhi, M. Perc and D. Ghosh, Chimera states in uncoupled neurons induced by a multilayer structure, Sci. Rep., 6 (2016), 39033.
    [11] X. Mao, X. Li, W. Ding, S. Wang, X. Zhou and L. Qiao, Dynamics of a multiplex neural network with delayed couplings, Appl. Math. Mech. (Eng. Edit.), (2021). doi: 10.1007/s10483-021-2709-6
    [12] D. Nikitin, I. Omelchenko, A. Zakharova, M. Avetyan, A. L. Fradkov and E. Schöll, Complex partial synchronization patterns in networks of delay-coupled neurons, Philos. Trans. Roy. Soc. A, 377 (2019), 20180128, 19 pp. doi: 10.1098/rsta.2018.0128
    [13] J. Sawicki, I. Omelchenko, A. Zakharova and E. Schoell, Delay controls chimera relay synchronization in multiplex networks, Phys. Rev. E, 98 (2018), 062224.
    [14] Z. Wang, S. Liang, C. A. Molnar, T. Insperger and G. Stepan, Parametric continuation algorithm for time-delay systems and bifurcation caused by multiple characteristic roots, Nonlinear Dynam., (2020). doi: 10.1007/s11071-020-05799-w
    [15] Inter-layer synchronization of periodic solutions in two coupled rings with time delay. Physica D (2019) 396: 1-11.
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