Nonlinear Dynamics

, Volume 92, Issue 3, pp 1197–1215 | Cite as

Dynamical stability in a delayed neural network with reaction–diffusion and coupling

  • Ling Wang
  • Hongyong Zhao
  • Chunlin Sha
Original Paper


In this paper, a delayed neural network with reaction–diffusion and coupling is considered. The network consists of two sub-networks each with two neurons. In the first instance, some parameter regions are identified by employing partial functional differential equation theory. Moreover, sufficient conditions of stationary bifurcation and Bogdanov–Takens bifurcation are also derived. Further, analytical results and illustrations are proved for the case where the unstable trivial equilibrium point becomes stable in the presence of reaction–diffusion terms with appropriate values. We emphasize that the non-trivial role of diffusions is enlarging the stability region in the system described by PDE, comparing with the corresponding system described by DDE. Finally, numerical simulations are carried out to verify the efficiency of the theoretical analysis and provide comparisons with some existing literature.


Delayed neural network Reaction–diffusion term Bifurcation Absolute stability Conditional stability 



The work is supported by National Natural Science Foundation of China under Grant 11571170 and Grant 61403193, as well as being sponsored by Natural Science Found of Changzhou Institute of Technology under Grant No. E3-6701-16-006, and NSF of China (11301264), The NSF of Jiangsu Province of China (BK20130779). The authors would also like to express our gratitude to Editor and the anonymous referees for their valuable comments and suggestions that led to truly significant improvement of the manuscript.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.College of Mathematics and Chemical EngineeringChangzhou Institute of TechnologyChangzhouChina

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