Asymptotical stability for fractional‐order Hopfield neural networks with multiple time delays

摘要

This paper is concerned with the asymptotical stability of fractional‐order Hopfield neural networks with multiple delays. The problem is actually a generalization of stability for linear fractional‐order delayed differential equations: 0CDtαX(t)=MX(t)+CX(t−τ)$$ {}_0#x0005E;C{mathrm{D}}_t#x0005E;{alpha }X(t)#x0003D; MX(t)#x0002B; CXleft(t-tau right) $$, which is widely studied when Arg(λM)>π2$$ mid mathrm{Arg}left({lambda}_Mright)mid frac{pi }{2} $$. However, the stability is rarely known when απ2π2$$ mid mathrm{Arg}left({lambda}_Mright)mid frac{pi }{2} $$. Afterward, by a linearization technique, a necessary and sufficient stability condition is also presented for fractional‐order Hopfield neural networks with multiple delays. The conditions are established by delay‐independent coefficient‐type criteria. Finally, several numerical simulations are given to show the effectiveness of our results.