Stability of Reaction-Diffusion Recurrent Neural Networks with Distributed Delays and Neumann Boundary Conditions on Time Scales

Stability Analysis of Second-Order Linear PDEs on Time Scales

“…Recent related studies have shown that time scales are not only a theoretical territory of mathematics, but also an efective tool to handle many practical matters [17][18][19][20]. Although extensive research has been conducted on the stability analysis of dynamic equations on time scales, most of them were limited to ordinary diferential equations, and few studies on the stability of PDEs on time scales were made [21][22][23]. To overcome this shortcoming, this study examines the stability of the second-order linear PDEs on time scales based on the Lyapunov functional method.…”

“…(1) Compared to the existing works [21][22][23], the PDEs under consideration is more general for that where both the difusion operator and second-order partial diferential terms are taking into account. (2) Based on the Lyapunov functional and inequality methods, the sufcient conditions of stability are presented, and the results are generalized that they can unify the continuous-time and discrete-time cases.…”

Stability analysis for periodic solutions of fuzzy shunting inhibitory CNNs with delays

“…In the past three decades, the cellular neural networks (CNNs) have gained a lot of popularity due to their local inter-connectivity and practical hardware implementation [1][2][3][4][5][6][7][8].…”

Existence and Exponential Stability of Equilibrium Point for Fuzzy BAM Neural Networks with Infinitely Distributed Delays and Impulses on Time Scales

“…To avoid the troublesomeness of studying the dynamical properties for continuous and discrete systems, respectively, it is meaningful to study that on time scales, which was initiated by Stefan Hilger in his Ph.D. thesis in order to unify continuous and discrete analysis. Lots of scholars have studied neural networks on time scales and obtained many good results [23][24][25][26][27][28][29]. For example, in [30], the authors considered the existence and global exponential stability of an equilibrium point for a class of fuzzy BAM neural networks with time-varying delays in leakage terms on time scales.…”