Neural Processing Letters

, Volume 50, Issue 3, pp 2493–2514 | Cite as

Dynamic Optimization of Neuron Systems with Leakage Delay and Distributed Delay via Hybrid Control

  • Shuo Shi
  • Min XiaoEmail author
  • Binbin Tao
  • Jinxing Lin
  • Zunshui Cheng


This paper proposes a neuron system with both leakage delay and distributed delay. Typical dynamics including the local stability and Hopf bifurcation analysis are investigated. Then, a hybrid controller is designed to control the Hopf bifurcation of the proposed system. By regarding the leakage delay as the bifurcation parameter and further probing into the associated characteristic equation, we find that the system can generate a Hopf bifurcation when the bifurcation parameter passes through some critical value. Besides, the controller is capable of altering the bifurcation point and achieving desirable dynamics by changing the feedback gain parameter. Finally, numerical simulations are illustrated to substantiate the theoretical analysis.


Neuron system Hopf bifurcation Oscillation Hybrid control Leakage delay Strong kernel 



This work is supported in part by the National Natural Science Foundation of China (Nos. 61573194, 61473158), and the Natural Science Foundation of Jiangsu Province of China (No. BK20181389).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of AutomationNanjing University of Posts and TelecommunicationsNanjingChina
  2. 2.School of Mathematics and PhysicsQingdao University of Science and TechnologyQingdaoChina

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