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Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays

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  • Xu, Changjin

Abstract

In this paper, a class of simplified bidirectional associative memory (BAM) neural networks with multiple delays are considered. By analyzing the associated characteristic transcendental equation, their linear stability is investigated and Hopf bifurcation is demonstrated. By applying Nyquist criterion, the length of delay which preserves the stability of the zero equilibrium is estimated. Some explicit results are derived for stability and direction of the bifurcating periodic orbit by using the normal form theory and center manifold arguments. Global existence of periodic orbits is also established by using a global Hopf bifurcation theorem for functional differential equations (FDE) and a Bendixson’s criterion for high-dimensional ordinary differential equations (ODE) due to Li and Muldowney. Finally, numerical simulations supporting the theoretical analysis are carried out.

Suggested Citation

  • Xu, Changjin, 2018. "Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 69-90.
    • Handle: RePEc:eee:matcom:v:149:y:2018:i:c:p:69-90
    DOI: 10.1016/j.matcom.2018.02.002
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    References listed on IDEAS

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    1. Zheng, Baodong & Zhang, Yazhuo & Zhang, Chunrui, 2008. "Global existence of periodic solutions on a simplified BAM neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1397-1408.
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    Cited by:

    1. Khoshnevisan, Ladan & Liu, Xinzhi & Salmasi, Farzad R., 2019. "Stability and Hopf bifurcation analysis of a TCP/RAQM network with ISMC procedure," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 255-273.
    2. Xiao, Lin & Yi, Qian & Zuo, Qiuyue & He, Yongjun, 2020. "Improved finite-time zeroing neural networks for time-varying complex Sylvester equation solving," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 246-258.
    3. Xu, Changjin & Liu, Zixin & Liao, Maoxin & Li, Peiluan & Xiao, Qimei & Yuan, Shuai, 2021. "Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 471-494.
    4. Wang, Yangling & Cao, Jinde & Huang, Chengdai, 2024. "Bifurcations of a fractional three-layer neural network with different delays: Delay-dependent and order-dependent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    5. Wang, Yangling & Cao, Jinde & Huang, Chengdai, 2022. "Exploration of bifurcation for a fractional-order BAM neural network with n+2 neurons and mixed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    6. Wang, Wenlong & Lin, Xiao & Zhang, Chunrui, 2021. "Resonant bifurcation of feed-forward chains and application in image contrast enhancement," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 294-307.
    7. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Yuan, Shuai, 2021. "Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Guo, Ying & Xiao, Qimei & Yuan, Shuai, 2019. "Influence of multiple time delays on bifurcation of fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 565-582.

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