Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms

Observer-Based Boundary Stabilization of Coupled Semilinear Reaction-Diffusion Neural Networks With Spatially Varying Coefficients via Event-Triggered Controller

The aim of this article is to propose an observer-based event-triggered Robin boundary control strategy for the exponential stabilization of the coupled semilinear reaction-diffusion neural networks with spatially varying coefficients. Toward this aim, we design an observer to estimate the value of system states by using some of these system values as the available measurement. An observer-based event-triggered boundary stabilizer is then presented to exponentially stabilize the considered systems with the Zeno behavior being excluded. Throughout this article, the main used method is backstepping, which yields an explicit expression of the control formulae. Moreover, we see that the proposed event-triggered boundary control scheme can ensure the desired level of control performance with fewer control law updates. A numerical example is finally given to illustrate the effectiveness of our proposed method.

Finite-Time Synchronization and H∞ Synchronization for Coupled Neural Networks With Multistate or Multiderivative Couplings

This article investigates the finite-time synchronization (FTS) and H∞ synchronization for two types of coupled neural networks (CNNs), that is, the cases with multistate couplings and with multiderivative couplings. By designing appropriate state feedback controllers and parameter adjustment strategies, some FTS and finite-time H∞ synchronization criteria for CNNs with multistate couplings are derived. In addition, we further consider the FTS and finite-time H∞ synchronization problems for CNNs with multiderivative couplings by utilizing state feedback control approach and selecting suitable parameter adjustment schemes. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed criteria.

Stability of Delayed Reaction-Diffusion Neural-Network Models With Hybrid Impulses via Vector Lyapunov Function

This article focuses on stability analysis of delayed reaction-diffusion neural-network models with hybrid impulses based on the vector Lyapunov function. First, several properties of a vector Halanay-type inequality are given to be the key ingredient for the stability analysis. Then, the Krasovskii-type theorems are established for sufficient conditions of exponential stability, which removes the common threshold of impulses in each neuron subsystem at every impulse time. It shows that the stability of neural networks can be retained with hybrid impulses involved in neural networks, and the synchronization of neural networks can be achieved by designing an impulsive controller, which allows the existence of impulsive perturbation in some nodes and time. Finally, the effectiveness of theoretical results is verified by numerical examples with a successful application to image encryption.

Fixed-time periodic stabilization of discontinuous reaction-diffusion Cohen-Grossberg neural networks

This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction-diffusion Cohen-Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction-diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction-diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.

Strictly intermittent quantized control for fixed/predefined-time cluster lag synchronization of stochastic multi-weighted complex networks

This article addresses the fixed-time (F-T) and predefined-time (P-T) cluster lag synchronization of stochastic multi-weighted complex networks (SMWCNs) via strictly intermittent quantized control (SIQC). Firstly, by exploiting mathematical induction and reduction to absurdity, a novel F-T stability lemma is proved and an accurate estimation of settling time (ST) is obtained. Subsequently, by virtue of the proposed F-T stability, some simple conditions that ensure the F-T cluster lag synchronization of SMWCNs are derived by developing a SIQC strategy. Furthermore, the P-T cluster lag synchronization is also explored based on a SIQC design, where the ST can be predefined by an adjustable constant of the controller. Note that the designed controllers here are simpler and more economical than the traditional design whose the linear part is still activated during the rest interval. Finally, two numerical examples are provided to verify the effectiveness of the theoretical results.

Stability and Synchronization of Nonautonomous Reaction-Diffusion Neural Networks With General Time-Varying Delays

This article investigates the stability and synchronization of nonautonomous reaction-diffusion neural networks with general time-varying delays. Compared with the existing works concerning reaction-diffusion neural networks, the main innovation of this article is that the network coefficients are time-varying, and the delays are general (which means that fewer constraints are posed on delays; for example, the commonly used conditions of differentiability and boundedness are no longer needed). By Green's formula and some analytical techniques, some easily checkable criteria on stability and synchronization for the underlying neural networks are established. These obtained results not only improve some existing ones but also contain some novel results that have not yet been reported. The effectiveness and superiorities of the established criteria are verified by three numerical examples.

The Relationship between Intelligent Image Simulation and Recognition Technology and the Health Literacy and Quality of Life of the Elderly

In order to explore the relationship between intelligent image recognition technology and the mentality and quality of life of the elderly, this paper combines intelligent image simulation technology to identify the behavior of the elderly, protect the safety of the elderly, and provide timely feedback on the adverse conditions of the elderly. Moreover, this paper improves the traditional intelligent image recognition algorithm, verifies the research method of this paper through experimental research, and puts forward corresponding suggestions. Through investigation and research, we can see that the level of health literacy of elderly patients with chronic diseases is low. Therefore, in the future health education, we should strengthen health education for elderly patients with chronic diseases, use different mass media to propagate health knowledge, and promote the formation of healthy lifestyles and behaviors for elderly patients with chronic diseases. At the same time, the experiment also verified that the intelligent image recognition technology proposed in this paper has a positive effect in improving the mentality and quality of life of the elderly.

Fuzzy System Based Medical Image Processing for Brain Disease Prediction

The present work aims to explore the performance of fuzzy system-based medical image processing for predicting the brain disease. The imaging mechanism of NMR (Nuclear Magnetic Resonance) and the complexity of human brain tissues cause the brain MRI (Magnetic Resonance Imaging) images to present varying degrees of noise, weak boundaries, and artifacts. Hence, improvements are made over the fuzzy clustering algorithm. A brain image processing and brain disease diagnosis prediction model is designed based on improved fuzzy clustering and HPU-Net (Hybrid Pyramid U-Net Model for Brain Tumor Segmentation) to ensure the model safety performance. Brain MRI images collected from a Hospital, are employed in simulation experiments to validate the performance of the proposed algorithm. Moreover, CNN (Convolutional Neural Network), RNN (Recurrent Neural Network), FCM (Fuzzy C-Means), LDCFCM (Local Density Clustering Fuzzy C-Means), and AFCM (Adaptive Fuzzy C-Means) are included in simulation experiments for performance comparison. Results demonstrate that the proposed algorithm has more nodes, lower energy consumption, and more stable changes than other models under the same conditions. Regarding the overall network performance, the proposed algorithm can complete the data transmission tasks the fastest, basically maintaining at about 4.5 s on average, which performs remarkably better than other models. A further prediction performance analysis reveals that the proposed algorithm provides the highest prediction accuracy for the Whole Tumor under DSC (Dice Similarity Coefficient), reaching 0.936. Besides, its Jaccard coefficient is 0.845, proving its superior segmentation accuracy over other models. In a word, the proposed algorithm can provide higher accuracy, a more apparent denoising effect, and the best segmentation and recognition effect than other models while ensuring energy consumption. The results can provide an experimental basis for the feature recognition and predictive diagnosis of brain images.

Stability of delayed inertial neural networks on time scales: A unified matrix-measure approach

This note introduces a unified matrix-measure concept to study the stability of a class of inertial neural networks with bounded time delays on time scales. The novel matrix-measure concept unifies the classic matrix-measure and the generalized matrix-measure concept. One sufficient global exponential stability criterion is obtained based on this key matrix-measure and no Lyapunov function is required. To make the stability performance better, another stability criterion in which more detailed information is involved has been acquired. The theoretical results in this note contain and extend some existing continuous-time and discrete-time works. A numerical example is given to show the validity of the results.