HOPF BIFURCATION OF A FRACTIONAL TRI-NEURON NETWORK WITH DIFFERENT ORDERS AND LEAKAGE DELAY

Yangling Wang, Jinde Cao and Chengdai Huang
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Yangling Wang: School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, P. R. China
Jinde Cao: School of Mathematics, Southeast University, Nanjing 210096, P. R. China3Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
Chengdai Huang: School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-14

Abstract: This paper focuses on the Hopf bifurcation of a fractional tri-neuron network with both leakage delay and communication delay under different fractional orders. By applying fractional Laplace transform, the stability theorem of linear autonomous system and Hopf bifurcation theorem, we obtain a class of asymptotic stability criterion of zero solution as well as delay-induced Hopf bifurcation conditions for the considered system. Simultaneously, the stability and Hopf bifurcation for tri-neuron network with single fractional order are also discussed as a special case of our proposed neural network model. Finally, a simulation example is given to illustrate the efficiency of the presented theoretical results in this paper.

Keywords: Fractional Tri-Neuron Network; Different Orders; Hopf Bifurcation; Stability; Leakage Delay and Communication Delay (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500451

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