Cognitive Neurodynamics

, Volume 12, Issue 6, pp 625–636 | Cite as

Suppressing bursting synchronization in a modular neuronal network with synaptic plasticity

  • JiaYi Wang
  • XiaoLi YangEmail author
  • ZhongKui Sun
Research Article


Excessive synchronization of neurons in cerebral cortex is believed to play a crucial role in the emergence of neuropsychological disorders such as Parkinson’s disease, epilepsy and essential tremor. This study, by constructing a modular neuronal network with modified Oja’s learning rule, explores how to eliminate the pathological synchronized rhythm of interacted busting neurons numerically. When all neurons in the modular neuronal network are strongly synchronous within a specific range of coupling strength, the result reveals that synaptic plasticity with large learning rate can suppress bursting synchronization effectively. For the relative small learning rate not capable of suppressing synchronization, the technique of nonlinear delayed feedback control including differential feedback control and direct feedback control is further proposed to reduce the synchronized bursting state of coupled neurons. It is demonstrated that the two kinds of nonlinear feedback control can eliminate bursting synchronization significantly when the control parameters of feedback strength and feedback delay are appropriately tuned. For the former control technique, the control domain of effective synchronization suppression is similar to a semi-elliptical domain in the simulated parameter space of feedback strength and feedback delay, while for the latter one, the effective control domain is similar to a fan-shaped domain in the simulated parameter space.


Bursting synchronization Synaptic plasticity Nonlinear delayed feedback control Modular neuronal network 



This work is partially supported by the National Natural Science Foundation of China (Grant No. 11572180), the Fundamental Funds Research for the Central Universities (Grant Nos. GK201602009, GK201701001).


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceShaanxi Normal UniversityXi’anPeople’s Republic of China
  2. 2.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

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