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Dynamics in a Delayed Neural Network Model of Two Neurons with Inertial Coupling

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  • Changjin Xu
  • Peiluan Li

Abstract

A delayed neural network model of two neurons with inertial coupling is dealt with in this paper. The stability is investigated and Hopf bifurcation is demonstrated. Applying the normal form theory and the center manifold argument, we derive the explicit formulas for determining the properties of the bifurcating periodic solutions. An illustrative example is given to demonstrate the effectiveness of the obtained results.

Suggested Citation

  • Changjin Xu & Peiluan Li, 2012. "Dynamics in a Delayed Neural Network Model of Two Neurons with Inertial Coupling," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:689319
    DOI: 10.1155/2012/689319
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    References listed on IDEAS

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    1. Huang, Chuangxia & Huang, Lihong & Yuan, Zhaohui, 2005. "Global stability analysis of a class of delayed cellular neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(3), pages 133-148.
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    Cited by:

    1. Yuan, Shilei & Wang, Yantao & Zhang, Xian & Wang, Xin, 2024. "H∞ anti-synchronization of switching inertial neural networks with leakage delays and mixed time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 619-647.
    2. Shengwei Yao & Huonian Tu, 2014. "Stability Switches and Hopf Bifurcation in a Coupled FitzHugh‐Nagumo Neural System with Multiple Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Samir Kumar Bhowmik & Feras M. Al Faqih & Md. Nazmul Islam, 2014. "A Note on Some Numerical Approaches to Solve a θ˙ Neuron Networks Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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