Dynamics analysis on a class of delayed neural networks involving inertial terms

Abstract

This paper explores a class of unbounded distributed delayed inertial neural networks. By introducing some new differential inequality analysis and abandoning the traditional order reduction technique, some new assertions are derived to verify the global exponential stability of the addressed networks, which improve and generalize some recently published articles. Finally, two cases of numerical examples and simulations are given to illustrate these analytical conclusions.

Stability of antiperiodic recurrent neural networks with multiproportional delays

“…Remark Although Gargi et al, Zhang and Tan, Huang et al, Huang, Liu, Wang, and Tan dealt with the stability, dissipative and almost periodicity on RNNs with multiproportional delays, they gave no point to the antiperiodicity of such neural networks. From this viewpoint, our results are essentially new and complement some corresponding published results.…”

“…Recently, by introducing unbounded time‐varying delays with proportional time, the investigation of delayed recurrent neural networks (RNNs) has been the new worldwide focus. Some of the reasons come from their fruitful applications in many engineering fields, for example, combinatorial optimization, fault diagnosis, signal processing, robotic, automatic control engineering, and so on …”

Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

“…On account of this, fractional order calculus was introduced into artificial neural network in past few decades, namely, fractional order neural networks (FNNs), which can describe the neurodynamics of human brain more effectively and accurately in view of the hereditary and memory possessed by fractional calculus. Hence, the consideration of its dynamic behaviors like synchronization and stability plays a significant role in both theoretical and application perspectives, see for instance previous studies . Bao and Cao gave sufficient conditions to ascertain projective synchronization conditions for real‐valued FNNs by means of fractional order differential inequality.…”

Anti-periodicity on high-order inertial Hopfield neural networks involving mixed delays

“…To the best of our knowledge, the dynamics analysis on inertial neural networks is usually to convert them into a first-order differential system by reducing order variable substitution under the assumption that the activation functions are bounded [15][16][17]. However, the authors in [12,[18][19][20][21] pointed out that the above method not only raises the dimension in the inertial neural networks system, but also increases huge amount of computation which makes it difficult to realize in practice. For the above reasons, the authors of [19,20] and [21], respectively, developed some non-reduced order techniques to investigate the stability and synchronization of inertial neural networks with different types of time delays.…”