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Dynamics in a delayed-neural network

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  • Yuan, Yuan

Abstract

In this paper, we consider a neural network of four identical neurons with time-delayed connections. Some parameter regions are given for global, local stability and synchronization using the theory of functional differential equations. The root distributions in the corresponding characteristic transcendental equation are analyzed, Pitchfork bifurcation, Hopf and equivariant Hopf bifurcations are investigated by revealing the center manifolds and normal forms. Numerical simulations are shown the agreements with the theoretical results.

Suggested Citation

  • Yuan, Yuan, 2007. "Dynamics in a delayed-neural network," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 443-454.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:2:p:443-454
    DOI: 10.1016/j.chaos.2006.01.018
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    Cited by:

    1. Yang, Xiaofan & Yang, Maobin & Liu, Huaiyi & Liao, Xiaofeng, 2008. "Bautin bifurcation in a class of two-neuron networks with resonant bilinear terms," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 575-589.
    2. Kundu, Amitava & Das, Pritha & Roy, A.B., 2016. "Stability, bifurcations and synchronization in a delayed neural network model of n-identical neurons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 12-33.
    3. Zhang, Chunrui & Zheng, Baodong, 2009. "Bifurcation in Z2-symmetry quadratic polynomial systems with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3078-3086.

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