DYNAMICAL ANALYSIS OF A SELF-CONNECTION FRACTIONAL-ORDER NEURAL NETWORK

Jun Yuan, Lingzhi Zhao, Chengdai Huang and Min Xiao
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Jun Yuan: School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, P. R. China
Lingzhi Zhao: School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, P. R. China
Chengdai Huang: School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China
Min Xiao: College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 06, 1-17

Abstract: This paper researches the problem of bifurcation for a ring fractional-order neural network (FONN) with self-connection delay and communication delay. Self-connection delay is firstly regarded as a bifurcation parameter to examine the bifurcations of the developed FONN, and the critical values of bifurcations with respect to self-connection delay are derived. Second, communication delay is further taken as a bifurcation parameter to investigate the bifurcations of the designed FONN, and the stability zones and bifurcation points are determined. It reveals that FONN exhibits excellent stability performance when electing a lesser value of them, and the stability performance is devastated and Hopf bifurcation arises upon taking a larger one. Eventually, the efficiency of the developed theory is appraised on account of numerical verifications.

Keywords: Self-Connection Delays; Communication Delay; Stability; Hopf Bifurcation; Fractional-Order Neural Networks (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501383

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