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

Abstract

This paper deals with a class of high-order inertial Hopfield neural networks involving mixed delays. Utilizing differential inequality techniques and the Lyapunov function method, we obtain a sufficient assertion to ensure the existence and global exponential stability of anti-periodic solutions of the proposed networks. Moreover, an example with a numerical simulation is furnished to illustrate the effectiveness and feasibility of the theoretical results.

Periodicity on Neutral-Type Inertial Neural Networks Incorporating Multiple Delays

“…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][15][16][17][18][19][20][21] extensively studied various dynamic behaviors of system (1) and its generalizations via applying the non-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][34][35][36][37][38][39][40] or INNs [3][4][5][6][7][8][9][11][12][13][14][15][17][18][19][20][21][30][31][32]. Compared with the results on exponential stability for the neutral-type neural networks (NTNNs) [26,29,39,41] and INNs [13,14,18,19], we give the exponential stability of the T-periodic solution for the NTINNs. (4) An instructive numerical simulation including comparisons is afforded to demonstrate the obtained theoretical results.…”