High-order Hopfield Neural Networks Research Articles

A Further Study of Almost Periodic Time Scales with Some Notes and Applications

We introduce three equivalent concepts of almost periodic time scales as a further study of the corresponding concept proposed in Li and Wang (2011) and several examples of almost periodic time scales which are not periodic are provided. Furthermore, the concepts of almost periodic functions are redefined under the sense of this new timescale concept. Finally, almost periodicity of Cauchy matrix for dynamic equations is proved under these new definitions. Based on these results, the existence of almost periodic solutions to a class of nonlinear dynamic equations is investigated by the almost periodicity of Cauchy matrix on almost periodic time scales. Besides, as an application, we apply our results to a class of high-order Hopfield neural networks.

Anti-periodic solution for impulsive high-order Hopfield neural networks with time-varying delays in the leakage terms

This paper presents new results on anti-periodic solutions for impulsive high-order Hopfield neural networks with time-varying delays in the leakage terms. By employing a novel proof, some criteria are derived for guaranteeing the existence and exponential stability of the anti-periodic solution, which are new and complement previously known results. Moreover, a numerical simulation is given to show the effectiveness.

GLOBAL EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS OF HIGH-ORDER HOPFIELD NEURAL NETWORKS WITH DISTRIBUTED DELAYS OF NEUTRAL TYPE

In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.

Mean Square Exponential Stability of Stochastic High-Order Hopfield Neural Networks with Time-Varying Delays

The paper considers the problems of global exponential stability for stochastic delayed high-order Hopfield neural networks with time-varying delays. By employing the linear matrix inequality(LMI) and the Lyapunov functional methods, we present some new criteria ensuring globally mean square exponential stability. The results impose constraint conditions on the network parameters of neural system independent. The results are applicable to all continuous non-monotonic neuron activation functions.

Dynamic analysis for high-order Hopfield neural networks with leakage delay and impulsive effects

This paper considers existence, uniqueness, and the global asymptotic stability for a class of High-order Hopfield neural networks with mixed delays and impulses. The mixed delays include constant delay in the leakage term (i.e., "leakage delay") and time-varying delays. Based on the Lyapunov stability theory, together with the linear matrix inequality approach and free-weighting matrix method, some less conservative delay-dependent sufficient conditions are presented for the global asymptotic stability of the equilibrium point of the considered neural networks. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the applicability of the result.

Almost Periodic Functions on Time Scales and Applications

We first propose the concept of almost periodic time scales and then give the definition of almost periodic functions on almost periodic time scales, then by using the theory of calculus on time scales and some mathematical methods, some basic results about almost periodic differential equations on almost periodic time scales are established. Based on these results, a class of high‐order Hopfield neural networks with variable delays are studied on almost periodic time scales, and some sufficient conditions are established for the existence and global asymptotic stability of the almost periodic solution. Finally, two examples and numerical simulations are presented to illustrate the feasibility and effectiveness of the results.

Existence and Exponential Stability of Anti-periodic Solutions of High-order Hopfield Neural Networks with Delays on Time Scales

On time scales, a class of delayed high-order Hopfield neural networks are considered. We establish some sufficient conditions on the existence and exponential stability of anti-periodic solutions for the following Hopfield neural networks with time-varying and distributed delays $$\begin{array}{l} x_i^{\Delta}(t)\,=\,-c_i(t)x_i(t)+\sum\limits^n_{j=1}a_{ij}(t)f_j\left(x_j(t-\gamma_{ij}(t))\right)\\ \,\quad\,\quad\,\quad\,\,+\,\sum\limits^n_{j=1} \sum\limits_{l=1}^{n}b_{ijl}(t)\int\limits_0^{\infty}k_{ij}(\theta)g_j(x_j(t-\theta))\Delta \theta \int\limits_0^{\infty}k_{il}(\theta)g_l(x_l(t-\theta))\Delta \theta\\ \,\quad\,\quad\,\quad\,\,+\,\quad I_i(t),\quad i=1,2,\ldots,n\end{array}$$ on time scales. Finally, an example is given to show the effectiveness of the proposed method and results.

Global Robust Exponential Stability of Uncertain Neutral High-Order Stochastic Hopfield Neural Networks with Time-Varying Delays

In this paper, a class of uncertain neutral high-order stochastic Hopfield neural networks with time-varying delays is investigated. By using Lyapunov-Krasovskii functional and stochastic analysis approaches, new and less conservative delay-dependent stability criteria is presented in terms of linear matrix inequalities to guarantee the neural networks to be globally robustly exponentially stable in the mean square for all admissible parameter uncertainties and stochastic perturbations. Numerical simulations are carried out to illustrate the main results.

The boundedness of high-order Hopfield neural networks with variable delays

In this paper, the uniformly boundedness and uniformly ultimately boundedness of high-order neural networks with time-varying delays are studied. Proper Lyapunov functionals and some analytic techniques are employed to derive the sufficient conditions under which the networks proposed are uniformly bounded and uniformly ultimately bounded. The results are shown to improve the results derived in [1] (Arik, 2004). Some examples are given to illustrate the correctness of our results.

Dynamics of high-order Hopfield neural networks with time delays

In this paper, the global exponential stability and the existence of periodic solution are studied for a class of high-order Hopfield neural networks (HHNNs) with time delays by employing Lyapunov method and linear matrix inequality (LMI) technique. Several simple sufficient conditions are given ensuring global exponential stability and the existence of periodic solution of HHNNs. The obtained results improve some previous works and do not require the symmetry of weight matrix. Finally, two illustrative examples are given to demonstrate the effectiveness of the obtained results.

Stationary oscillation for high-order Hopfield neural networks with time delays and impulses

We investigate stationary oscillation for high-order Hopfield neural networks with time delays and impulses. In a recent paper [J. Zhang, Z. J. Gui, Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays, Journal of Computational and Applied Mathematics 224 (2008) 602–613], the authors claim that they obtain a criterion of existence, uniqueness, and global exponential stability of periodic solution (i.e. stationary oscillation) for high-order Hopfield neural networks with time delays and impulses. In this paper, we point out that the main result of the recent paper is unture, and present a new sufficient condition of stationary oscillation for the neural networks. A numerical example is given to illustrate the effectiveness of the obtained result.

Existence and Exponential Stability of Periodic Solution of High-Order Hopfield Neural Network with Delays on Time Scales

On time scales, by using the continuation theorem of coincidence degree theory and constructing some suitable Lyapunov functions, the periodicity and the exponential stability are investigated for a class of delayed high-order Hopfield neural networks (HHNNs), which are new and complement of previously known results. Finally, an example is given to show the effectiveness of the proposed method and results.

Anti-periodic solutions for high-order Hopfield neural networks

In this paper high-order Hopfield neural networks (HHNNs) with time-varying delays are considered. Sufficient conditions for the existence and exponential stability of anti-periodic solutions are established, which are new and complement previously known results.

Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, the global exponential stability and periodicity are investigated for a class of delayed high-order Hopfield neural networks (HHNNs) with impulses, which are new and complement previously known results. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results. The numerical simulation shows that our models can occur in many forms of complexities including periodic oscillation and the Gui chaotic strange attractor.

Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks

This paper is concerned with the existence and exponential stability of positive almost periodic solutions of high-order Hopfield neural networks (HHNNs) with time-varying delays. Some sufficient conditions for the existence and exponential stability of positive almost periodic solutions are established.

New convergence behavior of high-order hopfield neural networks with time-varying coefficients

In this paper the convergence behavior of the delayed high-order Hopfield neural networks (HHNNs) with time-varying coefficients are considered. Some sufficient conditions are established to ensure that all solutions of the networks converge to zero point, which are new and complement of previously known results.

Existence and exponential stability of almost-periodic solutions for high-order Hopfield neural networks

In this paper high-order Hopfield neural networks (HHNNs) with continuously distributed delays are considered. Several sufficient conditions for the existence and exponential stability of the almost-periodic solutions are established by using a fixed point theorem, Lyapunov functional method and differential inequality techniques. The results of this paper are new and complement previously known ones.

Stability analysis of analogue neural networks

A high-order analogue Hopfield neural network is incorporated to obtain optimal or near optimal solutions to types of nonlinear programming problems. The nonlinear functional analysis gives two sufficient conditions for the proposed neural network to obtain the Lyapunov stability solutions.