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

Abstract

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.

Event‐triggered pinning control for passivity and synchronization of directly coupled delayed reaction‐diffusion neural networks

“…Remark 7. Lately, many scholars have paid much attention to dynamical behaviors of CNNs, and numerous passivity and synchronization results have been obtained, [32][33][34][35][36][37][38][39][40][41][42] and applied successfully to image encryption and secure communication. 32,33 Notice that RDP is neglected in previous works above, and models of CNNs are built based on a set of ordinary differential equations, which only depend on time variable for the nodes' state.…”

“…">We build a general model of directly CDRDNNs, where dimensions of input and output vectors are different. Compared with previously published literature, 34‐42 the presented model includes reaction‐diffusion term and time‐varying delay, and with directly coupled in our article (i.e., directly CDRDNNs), which is more general and comprehensive, and can reveal more networks well in practice. Passivity and synchronization criteria for directly CDRDNNs are acquired by means of designing appropriate pinning control with event‐triggered mechanism.…”

“…Practically speaking, coupled neural networks (CNNs) belong to a member of CNs, and have been successfully employed in various fields such as image encryption and secure communication 32,33 . Thus, a number of scholars have devoted to investigating CNNs, and passivity and synchronization results have been obtained recently 34‐40 . In Reference 34, synchronization conditions were obtained for delayed CNNs through designing delayed impulsive controllers.…”

“…We build a general model of directly CDRDNNs, where dimensions of input and output vectors are different. Compared with previously published literature, [34][35][36][37][38][39][40][41][42] the presented model includes reaction-diffusion term and time-varying delay, and with directly coupled in our article (i.e., directly CDRDNNs), which is more general and comprehensive, and can reveal more networks well in practice.…”

“…32,33 Thus, a number of scholars have devoted to investigating CNNs, and passivity and synchronization results have been obtained recently. [34][35][36][37][38][39][40] In Reference 34, synchronization conditions were obtained for delayed CNNs through designing delayed impulsive controllers. Reference 35 first studied directly coupled networks in virtue of the normalized left eigenvector approach, which was developed for synchronization control criteria.…”