Abstract
The classical Hopefield neural networks have obvious symmetry, thus the study related to its dynamic behaviors has been widely concerned. This research article is involved with the neutral-type inertial neural networks incorporating multiple delays. By making an appropriate Lyapunov functional, one novel sufficient stability criterion for the existence and global exponential stability of T-periodic solutions on the proposed system is obtained. In addition, an instructive numerical example is arranged to support the present approach. The obtained results broaden the application range of neutral-types inertial neural networks.
Highlights
Since the global exponential stability of the T-periodic solutions on neutral-type inertial neural networks (NTINNs) involving multiple delays has never been studied, one can see that all the conclusions in references [42–69]
We researched the problem of the periodic solutions on NTINNs involving multiple delays
We obtained the existence of periodic solutions and their exponential stability
Summary
The well-known inertial neural networks (INNs) were first introduced by Babcock and Westervelt [1,2], and can be expressed as the following functional differential equations: Academic Editors: Quanxin Zhu, Fanchao Kong and Zuowei Cai n n k =1 k =1. For the sake of avoiding the traditional reduced-order method, the authors proposed several new criteria for the stability and synchronization of the system (1) in [12,13] through making a new Lyapunov functional On this basis, references [14–21] extensively studied various dynamic behaviors of system (1) and its generalizations via applying the non-reduced order approach. Enlightened by the above arguments, our major purpose in this article is to investigate the existence and stability of periodic solutions on NTINNs involving multiple delays through constructing a new and appropriate Lyapunov functional to replace the traditional reduced-order approach. (2) Under certain assumptions, by exploiting the non-reduced order approach, one new sufficient stability criterion to guarantee the existence and stability of the T-periodic solutions on system (3) is gotten for the first time; (3) NTINNs here are second-order and involve multiple neutral delays, which are different from the traditional NNs [33–40].
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