Exponential synchronization and Ulam-Hyers-Rassias stability for n spiking neural networks with time delays via different controller matrix over a time scale

Abstract

The synchronization and stability issues of a network of $n$ spiking neural networks with time delays over a time scale are thoroughly examined in this study, presenting a pioneering exploration in this domain. Notably, this research is the first to investigate the synchronization and Ulam-Hyers-Rassias stability of spiking neural networks and of a network of $n$ such networks, thus filling a significant gap in the existing literature. To attain Ulam-Hyers-Rassias stability, exponential synchronization and establish a connection between them, we define two different control strategies: feedback control and output control protocols. This approach is founded on time scale theory, the Halanay inequality, unified matrix-measure theory, and matrix norm theory. Simulated examples on various time domains are provided in the last section to demonstrate the effectiveness and wide range of applications of these findings.