Detecting bifurcations in a fractional-order neural network with nonidentical delays via Cramer's rule

被引:9
|
作者
Wang, Huanan [1 ]
Huang, Chengdai [1 ]
Liu, Heng [2 ]
Cao, Jinde [3 ,4 ]
机构
[1] Xinyang Normal Univ, Sch Math & Stat, Xinyang 464000, Peoples R China
[2] Guangxi Minzu Univ, Sch Math & Phys, Nanning 530006, Peoples R China
[3] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China
[4] Yonsei Univ, Yonsei Frontier Lab, Seoul 03722, South Korea
基金
中国国家自然科学基金;
关键词
Fractional-order neural network; Hopf bifurcation; quartic transcendence term; Cramer's rule; SYSTEMS; STABILITY;
D O I
10.1016/j.chaos.2023.113896
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This article is dedicated to reseaching the bifurcations of a fractional-order neural network (FONN) with nonidentical self-connection and comunication delays. In accordance with eigenvalue analysis, we apply Cramer's rule to ingeniously calculate the specific value of the bifurcation point of an equation set with quartic transcendence term. It is noteworthy that the method proposed in this article is more concise than the existing methods for solving higher-order transcendental terms, and has a certain degree of generalization, which can be applied to the case involving n degree transcendental terms. Furthermore, it detects that the devised FONN can ameliorate dramatically the stability attributions in comparison with its integer-order counterpart. This article ultimately provides two experimental fruits for bifurcation caused by different delays to underpin the correctness of the developed methodology.
引用
收藏
页数:15
相关论文
共 50 条
  • [31] Bifurcation analysis of a fractional-order Cohen-Grossberg neural network with three delays
    Huang, Chengdai
    Mo, Shansong
    Liu, Heng
    Cao, Jinde
    CHINESE JOURNAL OF PHYSICS, 2024, 88 : 360 - 379
  • [32] Fractional-order discontinuous systems with indefinite LKFs: An application to fractional-order neural networks with time delays
    Udhayakumar, K.
    Rihan, Fathalla A.
    Rakkiyappan, R.
    Cao, Jinde
    NEURAL NETWORKS, 2022, 145 : 319 - 330
  • [33] Detections of bifurcation in a fractional-order Cohen-Grossberg neural network with multiple delays
    Huang, Chengdai
    Mo, Shansong
    Cao, Jinde
    COGNITIVE NEURODYNAMICS, 2024, 18 (03) : 1379 - 1396
  • [34] Positivity and Stability of Fractional-Order Coupled Neural Network with Time-Varying Delays
    Gong, Jiyun
    Qiu, Hongling
    Shen, Jun
    ELECTRONICS, 2023, 12 (23)
  • [35] Bifurcation Analysis of a Fractional-Order Bidirectional Associative Memory Neural Network with Multiple Delays
    Wang, Huanan
    Huang, Chengdai
    Cao, Jinde
    Abdel-Aty, Mahmoud
    COGNITIVE COMPUTATION, 2023, 15 (06) : 2132 - 2151
  • [36] Fractional-Order Deep Backpropagation Neural Network
    Bao, Chunhui
    Pu, Yifei
    Zhang, Yi
    COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE, 2018, 2018
  • [37] Synchronization of fractional-order memristive neural networks with time delays
    Chen, Chong
    Ding, Zhixia
    Li, Sai
    Wang, Liheng
    2019 CHINESE AUTOMATION CONGRESS (CAC2019), 2019, : 2754 - 2759
  • [38] Dynamics of Fractional-Order Neural Networks With Discrete and Distributed Delays
    Si, Lingzhi
    Xiao, Min
    Jiang, Guoping
    Cheng, Zunshui
    Song, Qiankun
    Cao, Jinde
    IEEE ACCESS, 2020, 8 (46071-46080): : 46071 - 46080
  • [39] A Novel Fractional-Order Cascade Tri-Neuron Hopfield Neural Network: Stability, Bifurcations, and Chaos
    Kumar, Pushpendra
    Lee, Tae H.
    Erturk, Vedat Suat
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2024, 23 (05)
  • [40] BIFURCATIONS EMERGING FROM DIFFERENT DELAYS IN A FRACTIONAL-ORDER PREDATOR-PREY MODEL
    Huang, Chengdai
    Li, Huan
    Chen, Xiaoping
    Cao, Jinde
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2021, 29 (02)