Dynamic Bifurcation Analysis of Incommensurate Fractional-Order Hopfield Neural Networks with Multiple Time Delays
DOI:
https://doi.org/10.15377/2409-5761.2025.12.11Keywords:
Stability analysis, Nonlinear dynamics, Dynamic bifurcation, Hopfield neural network, Three nonidentical delays, Fractional-order neural networks, Adams-Bashforth-Moulton methodAbstract
This study extends a traditional neural network model to an asymmetric Hopfield model incorporating triple time delays through a combined qualitative and quantitative analytical approach. The system is first linearized using Taylor series expansion, followed by the determination of bifurcation points in the resulting system of equations containing quadratic transcendental terms. An improved Adams-Bashforth-Moulton predictor-corrector method is employed for discretization analysis. Theoretical findings are validated through three numerical case studies, with further examination of how time delays influence the system’s dynamic behavior.
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