Periodic solution for neutral-type inertial neural networks with time-varying delays

Abstract

In this paper the problems of the existence and stability of periodic solutions of neutral-type inertial neural networks with time-varying delays are discussed by applying Mawhin’s continuation theorem and Lyapunov functional method. Finally, two numerical examples are given to illustrate our theoretical results.

On existence conditions for periodic solutions to a differential equation with constant argument

“…For more details, see, e.g., [19][20][21]. The problems of periodic solutions for neutral-type inertial neural networks with single and multiple variables delays are investigated in [22][23][24].…”

Periodicity on Neutral-Type Inertial Neural Networks Incorporating Multiple Delays

“…Especially in the application of NNs, periodic phenomenon is one of the most important dynamic behaviors to describe the symmetry of the Hopefield neural networks model, and the existence and stability of periodic solutions will help us to understand the asymptotic behavior of mathematical biological systems. Therefore, it is a very meaningful thing to research the existence and stability of periodic solutions [24,32]. However, few researches have discussed the periodic problem of the following NTINNs involving multiple delays:…”

“…(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.…”

New approaches for periodic wave solutions of a non-Newtonian filtration equation with variable delay

“…After that, more related papers for non-Newtonian filtration equation and related nonlinear equation appeared, see e.g. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”