Stability Analysis and Application for Delayed Neural Networks Driven by Fractional Brownian Noise

Fast synchronization control and application for encryption-decryption of coupled neural networks with intermittent random disturbance

In this paper, we design a new class of coupled neural networks with stochastically intermittent disturbances, in which the perturbation mechanism is different from other existed random neural networks. It is significant to construct the new models, which can simulate a class of the real neural networks in the disturbed environment, and the fast synchronization control strategies are studied by an adjustable parameter α. A controller with coupling signal is designed to study the exponential synchronization problem, meanwhile, another effective controller with not only adjustable synchronization rate but also with infinite gain avoided is used to investigate the preset-time synchronization. The fast synchronization conditions have been obtained by Lyapunov stability principle, Laplacian matrix and some inequality techniques. A numerical example shows the effectiveness of the control schemes, and the different control factors for synchronization rate are given to discuss the control effect. In particular, the image encryption-decryption based on drive-response networks has been successfully applied.

Enhancing economic competitiveness analysis through machine learning: Exploring complex urban features

Urban economic competitiveness is a fundamental indicator for assessing the level of urban development and serves as an effective approach for understanding regional disparities. Traditional economic competitiveness research that relies solely on traditional regression models and assumes feature relationship theory tends to fall short in fully exploring the intricate interrelationships and nonlinear associations among features. As a result, the study of urban economic disparities remains limited to a narrow range of urban features, which is insufficient for comprehending cities as complex systems. The ability of deep learning neural networks to automatically construct models of nonlinear relationships among complex features provides a new approach to research in this issue. In this study, a complex urban feature dataset comprising 1008 features was constructed based on statistical data from 283 prefecture-level cities in China. Employing a machine learning approach based on convolutional neural network (CNN), a novel analytical model is constructed to capture the interrelationships among urban features, which is applied to achieve accurate classification of urban economic competitiveness. In addition, considering the limited number of samples in the dataset owing to the fixed number of cities, this study developed a data augmentation approach based on deep convolutional generative adversarial network (DCGAN) to further enhance the accuracy and generalization ability of the model. The performance of the CNN classification model was effectively improved by adding the generated samples to the original sample dataset. This study provides a precise and stable analytical model for investigating disparities in regional development. In the meantime, it offers a feasible solution to the limited sample size issue in the application of deep learning in urban research.

A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks

The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.

Predefined-time synchronization of coupled neural networks with switching parameters and disturbed by Brownian motion

This article focuses on predefined time synchronization problem for a class of signal switching neural networks with time-varying delays. In the network models, we not only consider the coupling characteristics in the following networks, but also consider the disturbance with standard Brownian motion. In the design of the controller, the control gain is designed as 1ɛ+T_p-t (t∈[T₀,T_p), ɛ is an optional smaller positive number), which avoids the infinite gain (the control gain is designed as 1T_p-t in other reference). In order to get the predefined time control law, a power function is multiplied to the Lyapunov functional, from which it can get an exponential upper bound function via the derivative and mathematical expectation operation. Utilizing the martingale theory and the method of Laplace matrix, some novel predefined time synchronization criteria are obtained for the leader-following neural networks, meanwhile the following networks can maintain the leader network after achieved synchronization. Based on the special network of the main system, five corollaries separately develop the predefined time synchronization results from different perspectives. An example with some simulation figures and computing results fully exhibits the effectiveness of the achieved synchronization scheme. In this case, although the error signal is disturbed by Brownian motion, the trace signal can still stably converge to zero by this control scheme, meanwhile the predefined-time control effect is achieved.

Cluster Synchronization of Coupled Neural Networks With Lévy Noise via Event-Triggered Pinning Control

Cluster synchronization means that all multiagents are divided into different clusters according to the equations or roles of nodes in a complex network, and by designing an appropriate algorithm, each cluster can achieve synchronization to a certain value or an isolated node. However, the synchronization values between different clusters are different. With a feedback controller based on the calculation of the control input value and a trigger condition leading to the updating instants, this article introduces the trigger mechanism and designs a new data sampling strategy to achieve cluster synchronization of the coupled neural networks (CNNs), which reduces the number of updates of the controller, thereby reducing unnecessary waste of limited resources. In addition, an example proposes a synchronization algorithm and gives iterative procedures to calculate the trigger instants and prove the validity of the theoretical results.

Quasisynchronization of Heterogeneous Dynamical Networks via Event-Triggered Impulsive Controls

The time-triggered impulsive control of complex homogeneous dynamical networks has received wide attention due to its occasional occupation of the communication channels. This article is devoted to quasisynchronization of heterogeneous dynamical networks via event-triggered impulsive controls with less channel occupation. Two kinds of triggered mechanisms, that is, the centralized event-triggered mechanism in which the control is updated based upon the state information of all nodes, and the distributed event-triggered mechanism where the control is updated according to the state information of each node and its neighboring node, are proposed, respectively, such that the synchronization error between the heterogeneous dynamical networks and a virtual target is not more than a nonzero bound. What is more, the Zeno behavior is shown to be excluded. It is found that the combination method of the event-triggered control and the impulsive control, that is, the distributed event-triggered impulsive control has the advantage of low-energy consumption and takes up many fewer communication channels over the time-triggered impulsive control. Two numerical examples are conducted to illustrate the effectiveness of the proposed event-triggered impulsive controls.

Cross-network propagation model of public opinion information and its control in coupled double-layer online social networks

Purpose

In modern society, considering the multi-channel of public opinion information (public opinion) propagation and its strong influence on social development, it is necessary to study its propagation law and discuss the intervention strategy in online social networks (OSN).

Design/methodology/approach

First, a conceptual model of double-layer OSN was constructed according to their structural characteristics. Then, a cross-network propagation model of public opinion in double-layer OSN was proposed and discussed its spreading characteristics through numerical simulations. Finally, the control strategy of public opinion, especially the timing and intensity of intervention were discussed.

Findings

The results show that the double-layer OSN promotes the propagation of public opinion, and the propagation of public opinion in double-layer OSN has the characteristics of that in two single-layer OSN. Compared with the intervention intensity, the regulator should give the priority to the timing of intervention and try to intervene in the early stage of public opinion propagation.

Practical implications

This study may help the regulators to respond to the propagation of public opinion in OSN more actively and reasonably.

Originality/value

This research has a deep comprehension of the cross-network propagation rules of public opinion and manages the propagation of public opinion.

Finite- and Fixed-Time Cluster Synchronization of Nonlinearly Coupled Delayed Neural Networks via Pinning Control

In this article, the cluster synchronization problem for a class of the nonlinearly coupled delayed neural networks (NNs) in both finite- and fixed-time cases are investigated. Based on the Lyapunov stability theory and pinning control strategy, some criteria are provided to ensure the cluster synchronization of the nonlinearly coupled delayed NNs in both finite-and fixed-time aspects. Then, the settling time for stabilization that is dependent on the initial value and independent of the initial value is estimated, respectively. Finally, we illustrate the feasibility and practicality of the results via a numerical example.

Optimal control of stochastic system with Fractional Brownian Motion

In this paper, we introduce a class of stochastic harvesting population system with Fractional Brownian Motion (FBM), which is still unclear when the stochastic noise has the character of memorability. Stochastic optimal control problems with FBM can not be studied using classical methods, because FBM is neither a Markov pocess nor a semi-martingale. When the external environment impact on the system of FBM, the necessary and sufficient conditions for the optimization are offered through the stochastic maximum principle, Hamilton function and ItÔ formula in our work. To illustrate our study, we provide an example to demonstrate the obtained theoretical results, which is the expansion of certainty population system.

Stabilization of Mode-Dependent Impulsive Hybrid Systems Driven by DFA With Mixed-Mode Effects

This paper is concerned with mode-dependent impulsive hybrid systems driven by deterministic finite automaton (DFA) with mixed-mode effects. In the hybrid systems, a complex phenomenon called mixed mode, caused in time-varying delay switching systems, is considered explicitly. Furthermore, mode-dependent impulses, which can exist not only at the instants coinciding with mode switching but also at the instants when there is no system switching, are also taken into consideration. First, we establish a rigorous mathematical equation expression of this class of hybrid systems. Then, several criteria of stabilization of this class of hybrid systems are presented based on semi-tensor product (STP) techniques, multiple Lyapunov-Krasovskii functionals, as well as the average dwell time approach. Finally, an example is simulated to illustrate the effectiveness of the obtained results.