Delay-dependent bifurcation conditions in a fractional-order inertial BAM neural network

Chengdai Huang, Huanan Wang, Jinde Cao and Heng Liu

Chaos, Solitons & Fractals, 2024, vol. 185, issue C

Abstract: This paper explores the stability and bifurcation of a Caputo fractional-order BAM neural network with time delay and inertia terms. Subsequently, the limitation in bifurcation characteristics of Caputo fractional-order delayed inertial BAM neural network (CFODIBAMNN) is surpassed. By analyzing the stability of the system without time delay, the direct method is applied that involves solving the eigenvalues to determine its stability. Ulteriorly, analyzing the system in the presence of time delays and choosing the time delay as the bifurcation parameter to identify the Hopf bifurcation properties of the system. Eventually, during the verifications, the critical values of bifurcation are accurately calculated, the fluctuation and phase diagrams for the ranges of different fractional order are simulated and the impact of fractional orders on system stability is analyzed.

Keywords: Stability; Hopf bifurcation; Caputo fractional derivative; Inertia term; Delayed BAM neural network (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924006581

DOI: 10.1016/j.chaos.2024.115106

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