Finite‐time synchronization of multi‐weighted fractional‐order coupled neural networks with fixed and adaptive couplings

Summary This article concentrates on the finite‐time synchronization (FTS) for multi‐weighted fractional‐order coupled neural networks (MFCNNs) with fixed and adaptive couplings. A new dynamic model, which involves coupled neural networks with fractional order and multi‐weighted couplings, is proposed. Furthermore, an adaptive law to adjust the coupling weights is devised to ensure the FTS of such a complex model. First, by using fractional‐order calculus properties and inequality techniques, a finite‐time fractional differential inequality is presented, which considerably extends the prior result. Second, by the Lyapunov stability theory and the fractional‐order inequality, several sufficient conditions are acquired to make sure the FTS for MFCNNs. Moreover, the influence of the system's order on the FTS is also uncovered. Finally, a numerical simulation example and a practical simulation example are provided to demonstrate the validity of the obtained criteria.