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The dependence of synchronization transition processes of coupled neurons with coexisting spiking and bursting on the control parameter, initial value, and attraction domain

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Abstract

As the value of a control parameter decreases, monostable bursting changes to monostable spiking via the coexistence of spiking and bursting in a Leech neuron model, and the attraction domain of the bursting decreases, while that of the coexisting spiking increases for coexisting behaviors. As the coupling strength increases, the two coupled Leech neurons with the coexisting spiking and bursting manifest transitions from non-synchronization to complete synchronization (CS) through a complex process, which is dependent of the values of the control parameter, cases of configurations (one neuron spiking and the other bursting, both bursting, and both spiking), and the initial values of the two neurons. The transition processes involve various spiking and bursting or chaos synchronization states for the first two cases given here, but contain only spiking patterns for the last case. Corresponding with the attraction domain, the probability of initial values that can lead to bursting patterns of CS decreases, but the probability of initial values that can induce spiking of CS increases for the former two cases, as the control parameter is decreased. This phenomenon can also be interpreted by the structure and volume of the attraction domain with which all initial values can only induce CS of spiking for case 3. The results may improve understanding of the synchronization dynamics of the coupled neurons with coexisting behaviors.

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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Huaguang Gu & Baobao Pan

  2. Mathematics and Statistics Institute, Chifeng University, Chifeng, 024000, China

    Yuye Li

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  1. Huaguang Gu
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  2. Baobao Pan
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Correspondence to Huaguang Gu.

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This work was supported by the National Natural Science Foundation of China under Grant Nos. 11372224 and 11402039 and the Fundamental Research Funds for Central Universities designated to Tongji University under Grant No. 1330219127.

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Gu, H., Pan, B. & Li, Y. The dependence of synchronization transition processes of coupled neurons with coexisting spiking and bursting on the control parameter, initial value, and attraction domain. Nonlinear Dyn 82, 1191–1210 (2015). https://doi.org/10.1007/s11071-015-2226-7

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  • DOI: https://doi.org/10.1007/s11071-015-2226-7

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