Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

Streszczenie

We investigate a fractional-order, two-delayed tri-neuron neural network, highlighting the notable absence of a direct connection between the first and third neurons. Our stability analysis uncovers important insights into the network’s dynamic behavior. We examine the stability of the model’s equilibrium points, showing that the fractional-order model with time delays enhances interactions and amplifies outcomes under both stable and unstable conditions, all through robust analysis with the Laplace transformation approach. By incorporating these time delays, we effectively represent the model’s long-term behavior. Our theoretical findings are validated through numerical simulations using the predictor-corrector method, with results compellingly presented in MATLAB, supporting the viability of our hypotheses.