Novel algebraic criteria on global Mittag–Leffler synchronization for FOINNs with the Caputo derivative and delay

Abstract

This paper focuses on the global Mittag-Leffler (M-L) synchronization for fractionalorder inertial neural networks (FOINNs) including the Caputo derivative and delay. By choosing an appropriate variable transformation, the considered system including the inertial term is transformed into two fractional-order nonlinearly coupled interconnected subsystems. Combining with the delayed-feedback controller, fractional Lyapunov functional approach and inequality analysis technique, multi sets of novel algebraic criteria on the global M-L synchronization between derive-response systems are established. The main prominent highlight of this paper is that the proposed results are characterized by the algebraic inequalities form, which can simplify the calculation and facilitate the test. Two numerical simulation examples validate the theoretical results.

Quasi‐projective and finite‐time synchronization of delayed fractional‐order BAM neural networks via quantized control

“…Consequently, introducing the quantized controller to save the control cost and reduce the tremendous workload are highly significant. It is worth mentioning that the quantized controllers in our paper can optimize information and avoid channel congestion compared with the controllers without quantization in previous studies 12–14,40 . This is the first time to investigate the QPS and FTS of DFOBAMNNs by employing quantized controllers.…”

“…Recently, plenty of excellent fruits on dynamical behaviors for FOBAMNNs have been published. [11][12][13][14][15][16] It is known to all that diverse applications of FOBAMNNs largely rest with their dynamic nature, peculiarly for synchronization. Synchronization indicates that the states of all the nodes within the systems are finally agreed upon via certain action.…”

“…The synchronous study of FOBAMNNs is an urgent priority. Recently, plenty of excellent fruits on dynamical behaviors for FOBAMNNs have been published 11–16 …”

“…It is worth mentioning that the quantized controllers in our paper can optimize information and avoid channel congestion compared with the controllers without quantization in previous studies. [12][13][14]40 This is the first time to investigate the QPS and FTS of DFOBAMNNs by employing quantized controllers.…”

New results of global Mittag-Leffler synchronization on Caputo fuzzy delayed inertial neural networks

“…In the Riemann-Liouville's sense, Gu et al [8] proposed the model of FOINNs with delays. [5] further submitted the basis for judging GMLS of FOINNs under the sense of Caputo, which was expressed in the form of algebraic inequality. In [11,17,20,21,23,28,33,34], various dynamic behaviors of NNs were discussed, including but not limited to, fixed-time synchronization, ML synchronization, lag synchronization, finite-time synchronization, exponential synchronization, quasisynchronization, asymptotic stability, mean-square exponential synchronization, and H ∞ synchronization.…”