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.
Highlights
The inertial neural networks model, which was first proposed by Babcock and Westerwelt [1, 2], is one of the other popular artificial neural network models used in a variety of application areas
Numerous works have been devoted to study the dynamic behaviors on inertial neural networks with time-varying delays and some excellent results are reported, for example, stability [3–5], Hopf bifurcation [6–11], and synchronization [12–14]
5 Conclusions In this paper, abandoning the traditional reduced order method, we explore the global convergence dynamics on a class of anti-periodic high-order inertial Hopfield neural networks with bounded time-varying delays and unbounded continuously distributed delays
Summary
The inertial neural networks model, which was first proposed by Babcock and Westerwelt [1, 2], is one of the other popular artificial neural network models used in a variety of application areas. Yao [30] studied the existence and global exponential stability of anti-periodic solutions for a class of proportional delayed high-order inertial Hopfield neural networks with time-varying delays. Few articles have considered the anti-periodic problem for the following high-order inertial Hopfield neural networks (HIHNNs) involving time-varying delays and continuously distributed delays:. Theorem 3.1 Under conditions (G1)–(G4), system (1.1) has a globally exponentially stable T-anti-periodic solution. + dij(t)Bj κj t – qij(t) θijl(t)Qj κj t – ηijl(t) Ql κl t – ξijl(t) σij(u)Kj κj(t – u) du j=1 nn σijl(u)Rj κj(t – u) du j=1 l=1. The anti-periodicity on high-order inertial Hopfield neural networks with bounded time-varying delays and unbounded continuously distributed delays have never been touched upon by using the nonreduced order method. The corresponding results of [17–21, 27, 29, 30] and [46–95] cannot be used to reveal the convergence of the anti-periodic solution of the system (4.1)
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