High-order Hopfield Neural Networks Research Articles

Dynamical analysis of high-order Hopfield neural network with application in WBANs

Given the increasing demand for privacy preservation of medical data, a novel medical image encryption scheme is proposed based on Invertible Neural Network (INN) in this paper. Firstly, a new High-Order Hopfield Neural Network (HOHNN) is designed to yield a cipher flow as the conditional input, thereby regulating the encryption process. Moreover, its intrinsic properties as well as various dynamic behaviors are both demonstrated through theoretical analysis and two-parameter Lyapunov exponential charts. Secondly, guided by a multi-objective loss function and a known prior distribution, the original medical image is encrypted into a noise-like cipher image through the proposed encryption scheme. Besides, it is worth mentioning that unlike the existing deep learning-based data encryption schemes, the decryption network shares the identical weight matrix and network structure with the corresponding encryption one in this work. Finally, extensive simulation experiments have validated the feasibility as well as the security of the proposed scheme.

The dynamics of octonion-valued neutral type high-order Hopfield neural networks with D operator

In this paper, the existence, uniqueness and global exponential stability of pseudo almost periodic solutions for a class of octonion-valued neutral type high-order Hopfield neural network models with D operator are established by using the Banach fixed point theorem and differential inequality techniques. Compared with most existing models, in this class of networks, all connection weights and activation functions are assumed to be octonion-valued functions except for time delays. And unlike most of the existing methods of studying octonion-valued neural networks, our method is a non-decomposition method, that is, the method of directly studying octonion-valued systems. The results and methods in this paper are new. In addition, an example and its numerical simulation are given to illustrate the feasibility of our results.

The measure pseudo almost-periodicty and automorphy in HOHNNs with time-varying delays

In this work, we prove some existence, global exponential stability and uniqueness results for measure pseudo almost periodic and automorphic solutions to a class of high-order Hopfield neural networks with delays. The main technique is based upon some appropriate composition theorems combined with the Banach contraction mapping principle. Finally, three numerical examples are given to illustrate the effectiveness of our results.

Anti-periodic synchronization of quaternion-valued high-order Hopfield neural networks with delays

<abstract><p>This paper proposes a class of quaternion-valued high-order Hopfield neural networks with delays. By using the non-decomposition method, non-reduced order method, analytical techniques in uniform convergence functions sequence, and constructing Lyapunov function, we obtain several sufficient conditions for the existence and global exponential synchronization of anti-periodic solutions for delayed quaternion-valued high-order Hopfield neural networks. Finally, an example and its numerical simulations are given to support the proposed approach. Our results play an important role in designing inertial neural networks.</p></abstract>

Weyl Almost Periodic Solutions in Distribution of Clifford-Valued Stochastic High-Order Hopfield Neural Networks with Delays on Time Scales

Weyl Almost Periodic Solutions in Distribution of Clifford-Valued Stochastic High-Order Hopfield Neural Networks with Delays on Time Scales

Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays

<abstract><p>In this paper, we consider a class of Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays whose coefficients are Clifford numbers except the time delays. Based on the Banach fixed point theorem and inequality techniques, we obtain the existence and global exponential stability of almost periodic solutions in distribution of this class of neural networks. Even if the considered neural networks degenerate into real-valued, complex-valued and quaternion-valued ones, our results are new. Finally, we use a numerical example and its computer simulation to illustrate the validity and feasibility of our theoretical results.</p></abstract>

Anti-periodic solutions on Clifford-valued high-order Hopfield neural networks with multi-proportional delays

Of concern is the dynamics of anti-periodic solutions on Clifford-valued high-order Hopfield neural networks (CVHOHNNs) with multi-proportional delays. By utilizing differential inequality techniques, Lyapunov method and a rigorous mathematical proof, we establish some sufficient criteria on the existence and global stability of anti-periodic solutions. Finally, a numerical example is offered to verify and extend the analytical results and visualize the interesting phenomenon.

$$(\mu ,\nu )-$$Pseudo Almost Automorphic Solutions of Neutral Type Clifford-Valued High-Order Hopfield Neural Networks with D Operator

The aim of this article is to study neutral type Clifford-valued high-order Hopfield neural networks with mixed delays and D operator. New criteria are established for the existence, uniqueness and global exponential stability of $$(\mu ,\nu )-$$ pseudo almost automorphic solutions of the considered model via Banach’s fixed point principle and differential inequality techniques. An example is given to show the effectiveness of the main new criteria.

Pseudo almost periodic solutions for quaternion-valued high-order Hopfield neural networks with time-varying delays and leakage delays on time scales

<abstract> This paper deals with a class of quaternion-valued high-order Hopfield neural networks with time-varying delays and leakage delays on time scales. Based on the Banach fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and global exponential stability of pseudo almost periodic solutions for the considered networks. The results of this paper are completely new. Finally, an example is presented to illustrate the effectiveness of the obtained results. </abstract>

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

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.

Almost periodic solutions of quaternion-valued neutral type high-order Hopfield neural networks with state-dependent delays and leakage delays

In this paper, we consider the existence and global exponential stability of almost periodic solutions for a class of quaternion-valued neutral type neural networks with state-dependent delays and leakage delays by a direct approach. That is, without decomposing the considered quaternion-valued systems into real-valued systems, by using the contraction mapping fixed point theorem, we obtain the existence of almost periodic solutions of the considered networks with state-dependent delays and leakage delays, and by the counter-evidence method, we obtain the global exponential stability of almost periodic solutions of the considered networks with discrete delays and leakage delays. When the time delays in the considered systems are proportional time delays, our existence results are still true. At the same time, when the considered systems degenerate into real-valued or complex-valued systems, our results are still new.

Global exponential stability on anti-periodic solutions in proportional delayed HIHNNs

ABSTRACT This article mainly explores a class of proportional delayed high-order inertial Hopfield neural networks (HIHNNs) with time-varying coefficients. Without using the reduced-order method, by combining Lyapunov function method with differential inequality approach, some sufficient criteria on the existence of anti-periodic solutions including its uniqueness and exponential stability are built up. The obtained results provide us some lights for designing a stable HIHNNs and complement some earlier publications. In addition, simulations show that the theoretical anti-periodic dynamics are in excellent agreement with the numerically observed behaviour.

Anti-periodic solutions for Clifford-valued high-order Hopfield neural networks with state-dependent and leakage delays

Anti-periodic solutions for Clifford-valued high-order Hopfield neural networks with state-dependent and leakage delays

Global exponential stability of high-order Hopfield neural networks with state-dependent impulses

In this paper, we discuss the stability of high-order Hopfield neural networks with state-dependent impulses. Under some necessary assumptions, that every solution of the considered system intersects each impulsive surface exactly once is proved. Meanwhile, by using B-equivalence method, the considered system can be simplified to a system with fixed-time impulses. Moreover, some sufficient criteria are derived to ensure the stability between high-order Hopfield neural networks with state-dependent impulses and the corresponding system with fixed-time impulses. The main results show that the stability of high-order Hopfield neural networks with state-dependent impulses maintains no matter the stable continuous subsystems with unstabilizing impulses or the unstable continuous subsystems with stabilizing impulses. Finally, some numerical examples are given to illustrate the effectiveness of our results.

Almost Periodic Functions on the Quantum Time Scale and Applications

In this paper, we first propose two types of concepts of almost periodic functions on the quantum time scale. Secondly, we study some basic properties of almost periodic functions on the quantum time scale. Thirdly, based on these, we study the existence and uniqueness of almost periodic solutions of dynamic equations on the quantum time scale by Lyapunov method. Then, we give an equivalent definition of almost periodic functions on the quantum time scale. Finally, as an application, we propose a class of high-order Hopfield neural networks on the quantum time scale and establish the existence and global exponential stability of almost periodic solutions of this class of neural networks.

Existence and Exponential Stability of Anti-Periodic Solutions for Inertial Quaternion-Valued High-Order Hopfield Neural Networks With State-Dependent Delays

This paper deals with a class of inertial quaternion-valued high-order Hopfield neural networks with state-dependent delays. Without decomposing the considered neural networks into real-valued systems, based on a continuation theorem of coincidence degree theory and the Wirtinger inequality, the existence of anti-periodic solutions of the networks is established. By constructing a suitable Lyapunov function, the global exponential stability of anti-periodic solutions of the networks is obtained. Finally, a numerical example is given to show the feasibility of our results.

Existence and Global Exponential Stability of Pseudo Almost Periodic Solution for Clifford- Valued Neutral High-Order Hopfield Neural Networks With Leakage Delays

In this paper, we are concerned with a class of Clifford-valued neutral high-order Hopfield neural networks with leakage delays. Although the multiplication of Clifford numbers does not satisfy the commutativity, which brings great difficulties to the study of Clifford-valued systems, we have found a method that does not decompose Clifford-valued systems into real-valued systems to study the existence and global exponential stability of pseudo-almost periodic solutions of this class of neural networks. Our results are completely new. Finally, two examples are given to illustrate the effectiveness and feasibility of our main results.

Periodic Solution for $$\nabla $$ ∇ -Stochastic High-Order Hopfield Neural Networks with Time Delays on Time Scales

In this paper, the comparison theorem and Gronwall’s inequality with $$\nabla $$ -derivative on time scales are constructed. Based on $$\nabla $$ -stochastic integration, the $$\nabla $$ -stochastic high-order Hopfield neural networks with time delays on time scales is introduced and studied. By using contraction mapping principal and differential inequality technique on time scales, some sufficient conditions for the existence and exponential stability of periodic solutions for a class of $$\nabla $$ -stochastic high-order Hopfield neural networks with time delays on time scales are established. Our results show that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors for periodicity. Finally, a numerical example is provided to illustrate the feasibility of our results. The results of this paper are completely new even if the time scale $$\mathbb {T}=\mathbb {R}$$ or $$\mathbb {Z}$$ .

Stability analysis for a class of impulsive high-order Hopfield neural networks with leakage time-varying delays

This work considers the existence, the uniqueness, and the global exponential stability, the uniform asymptotic stability, the global asymptotic stability and the uniform stability, of a class of impulsive high-order Hopfield neural networks with distributed delays and leakage time-varying delays. The existence of a unique equilibrium point is proved by using contraction mapping principle theorem. By finding suitable Lyapunov–Krasovskii functional, some sufficient conditions are derived ensuring same kinds of stability. Finally, we analyze some numerical examples proving the efficiency of our theoretical results.

Anti-periodic Solutions for Quaternion-Valued High-Order Hopfield Neural Networks with Time-Varying Delays

In this paper, quaternion-valued high-order Hopfield neural networks (QVHHNNs) with time-varying delays are considered. Theoretically, a QVHHNN can be separated into four real-valued systems, forming an equivalent real-valued system. By using a novel continuation theorem of coincidence degree theory and constructing an appropriate Lyapunov function, some sufficient conditions are derived to guarantee the existence and global exponential stability of anti-periodic solutions for QVHHNN, which are new and complement previously known results.