Nonlinear Dynamics

, Volume 96, Issue 4, pp 2509–2522 | Cite as

Nonlinear delayed feedback control of synchronization in an excitatory–inhibitory coupled neuronal network

  • Xiaohan Zhang
  • Shenquan LiuEmail author
Original Paper


We explore nonlinear time-delayed feedback as a technique for the control of synchronization in excitatory–inhibitory coupled neuronal networks. The feedback signal can be expressed in two forms: differential feedback control and direct feedback control, to suppress bursting synchronization. In the two-dimensional plane of feedback strength and time delay, domains of effective synchronization suppression are described. For these two different types of nonlinear feedback, numerical simulations yield completely different results: The differential feedback is noninvasive, but it has a fragile robust performance. However, the direct feedback is robust against stimulation parameter variations, but it is invasive. Furthermore, electromagnetic induction is introduced by calculating the magnetic flux on membrane, and how it affects nonlinear time-delayed feedback control to suppress bursting synchronization is explored. We show that desynchronization effect of the differential feedback can be enhanced by appropriate electromagnetic induction. And desynchronization effect of the direct feedback is maintained by a small electromagnetic induction intensity, and no longer works once it exceeds a critical value. These presented results are expected to facilitate us to control abnormal brain synchrony, and promote the applications of the nonlinear feedback control scheme in practical clinical treatment.


Excitatory–inhibitory coupled neuronal networks Nonlinear feedback control Electromagnetic induction Bursting synchronization 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 11572127 and 11172103).

Compliance with ethical standards

Conflict of interest statement

We declare that we have no conflict of interest concerning the publication of this manuscript.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of MathematicsSouth China University of TechnologyGuangzhouChina

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