Exponential synchronization of memristor-based recurrent neural networks with time delays

In this paper, the synchronization control of a general class of memristor-based recurrent neural networks with time delays is investigated. A delay-dependent feedback controller is derived to achieve the exponential synchronization based on the drive-response concept, linear matrix inequalities (LMIs) and Lyapunov functional method. Finally, a numerical example is given to illustrate the derived theoretical results.     

Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities

This paper addresses the problems of stability and synchronization for a class of Markovian jump neural networks with partly unknown transition probabilities. We first study the stability analysis problem for a single neural network and present a sufficient condition guaranteeing the mean square asymptotic stability. Then based on the Lyapunov functional method and the Kronecker product technique, the chaos synchronization problem of an array of coupled networks is considered. Both the stability and the synchronization conditions are delay-dependent, which are expressed in terms of linear matrix inequalities. The effectiveness of the developed methods is shown by simulation examples.     

具有切换概率分布的概率布尔网络的依分布稳定和镇定

布尔网络作为研究基因调控网络的一种重要模型,近年来引起了国内外很多学者的广泛关注.本文利用代数状态空间表示方法,研究具有切换概率分布的概率布尔网络的依分布稳定和镇定问题.首先,回顾针对切换布尔网络稳定性分析的现有的研究结果.其次,给出具有切换概率分布的概率布尔网络依分布稳定的定义,并利用矩阵的半张量积建立具有切换概率分布的概率布尔网络的代数表示.再次,基于该代数表示,建立具有切换概率分布的概率布尔网络的依分布稳定的充分必要条件.最后,给出具有切换概率分布的概率布尔控制网络镇定问题可解的充要条件,并给出相应的控制设计方法.     

Stability and stabilization of Boolean networks with impulsive effects

This paper investigates the stability and stabilization of Boolean networks with impulsive effects. After giving a survey on semi-tensor product of matrices, we convert a Boolean network with impulsive effects into impulsive discrete-time dynamics. Then, some necessary and sufficient conditions are given for the stability and stabilization of Boolean networks with impulsive effects. Finally, examples are provided to illustrate the efficiency of the obtained results.     

Novel decentralized adaptive strategies for the synchronization of complex networks

This paper is concerned with the analysis of the synchronization of networks of nonlinear oscillators through an innovative local adaptive approach. In particular, time-varying feedback coupling gains are considered, whose gradient is a function of the local synchronization error over each edge in the network. It is shown that, under appropriate conditions, the strategy is indeed successful in guaranteeing the achievement of a common synchronous evolution for all oscillators in the network. The theoretical derivation is complemented by its validation on a set of representative examples.     

随机阿波罗网络的动力学同步研究

应用随机交叉边法在不改变网络度分布的情况下研究了随机阿波罗网络（Random Apollonian network）的拓扑结构与其上所加的动力学系统同步行为间的关系,发现在一定范围内,随着网络聚集系数的减小,网络的同步能力增加,但当继续减小聚集系数时,同步能力又会迅速减弱。     

Passive stability and synchronization of complex spatio-temporal switching networks with time delays

In this paper, a new model of complex spatio-temporal switching network is established. Each subsystem of the network at a different time interval corresponds to a different switching mode. Switching the signal depends on both the instant time t and the index of node i. Based on passivity property, the passive stability and synchronization of this kind of network with time delays are taken into account. An example and simulation results are included.     

Passivity-based control and synchronization of general complex dynamical networks

This paper presents some sufficient conditions for complex dynamical networks with and without coupling delays in the state to be passive. Based on the passivity property and linearization, control and synchronization of the dynamical networks are also addressed. An example and simulation results are included.     

Stability measures of some static interconnection networks

It is important that a communication service has to service dependability by high level. Many affairs cause failures in a network. Destroying nodes or links in communication network, cable cuts, node interruptions, software errors or hardware failures and transmission failure at various points, human error or accident and can interrupt service for long periods of time. At the beginning a communication network, requiring greater degree of stability or less vulnerability. In this work, various stability measures of a communication network are defined and the stability measures of some static interconnection networks which are known long times and w-star networks that are a new graph class, are given.     

Exponential synchronization of Cohen-Grossberg neural networks via periodically intermittent control

In this paper, a class of Cohen-Grossberg neural networks with time-varying delays are studied by designing a periodically intermittent controller. Some novel and effective exponential synchronization criteria are derived by applying some analysis techniques. These results generalize a few previous known results and remove some restrictions on control width and time-delays. Finally, a chaotic Cohen-Grossberg neural network is represented to show the effectiveness and feasibility of our results.     

Stability estimation of PFM-type pulsed neural networks

This study aims at development of practical stability estimation method for PFM-type pulsed neural networks. We already derived a graphical analysis method for a single-unit PFM-type neural network. In this paper, we extend this method so that it can deal with stability estimation of networks with multi-unit PFM-type pulsed neurons by using the concept of Generalised Nyquist Stability Criterion. We also illustrate numerical examples that show the extended method is not excessively conservative but still effectively estimates the non-existence of limit cycles.     

Temporal coding with synchronization and acceleration as complementary mechanisms

Temporal coding requires an appropriate combination of synchronizing and desynchronizing mechanisms. We study temporal coding with a desynchronizing mechanism, referred to as acceleration, that causes the units of the network to oscillate with higher phase velocity in case of stronger and/or more coherent input. Recently, it was demonstrated that combining synchronization with acceleration implies a competition for coherence that has a profound and favorable effect on the segmentation of overlapping patterns. Here, we demonstrate, first, an effect of coupling non-identical oscillators. Second, we discuss how including inhibitory couplings enforces the segmenting effect of acceleration. Third, we show how stronger couplings between the units of a pattern may support it in winning this competition for coherence.     

Service networks with multichannel nodes in a random environment

Service networks with multichannel nodes of semi-Markovian type are considered. The parameters of a source of demands depend on the state of the Markovian random environment. For the process of servicing demands, the conditions of existence of a stationary mode are found, and the properties of stationary distribution in terms of spectral characteristics of the routing matrix are investigated. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 167–172, January–February, 2000.     

Analysis of synchronization in a supermarket refrigeration system

In a supermarket refrigeration, the temperature in a display case, surprisingly, influences the temperature in other display cases. This leads to a synchronous operation of all display cases, in which the expansion valves in the display cases turn on and off at exactly the same time. This behavior increases both the energy consumption and the wear of components. Besides this practical importance, from the theoretical point of view, synchronization, likewise stability, Zeno phenomenon, and chaos, is an interesting dynamical phenomenon. The study of synchronization in the supermarket refrigeration systems is the subject matter of this work. For this purpose, we model it as a hybrid system, for which synchronization corresponds to a periodic trajectory.To examine whether it is stable, we transform the hybrid system to a single dynamical system defined on a torus. Consequently,we apply a Poincar ′e map to determine whether this periodic trajectory is asymptotically stable. To illustrate, this procedure is applied for a refrigeration system with two display-cases.     

Stability bounds in networks with dynamic link capacities

We address the problem of stability in networks where the link capacities can change dynamically. We show that every network running a greedy scheduling policy is universally stable at any injection rate r<1/(Cd), where d is the largest number of links crossed by any packet and C is the maximum link capacity. We also show that system-wide time priority scheduling policies are universally stable at any injection rate r<1/(C(d−1)).     

On robust synchronization of nonlinear systems with application to grid integration of renewable energy sources

Many systems in the natural and physical world often work in unison with similar other systems. This process of simultaneous operation is known as synchronization. In the past few decades, owing to this phenomenon’s importance, extensive research efforts have been made. However, many of the existing results consider the systems are identical and/or linear time-invariant, while practical systems are often nonlinear and nonidentical for various reasons. This observation motivated several recent studies on the synchronization of nonidentical (i.e., heterogeneous) nonlinear systems. This paper summarizes some recent results on the synchronization of heterogeneous nonlinear systems, as developed in the thesis (Ahmed 2016). First, the results on the synchronization of a particular class of robustly stable nonlinear systems are presented. Then, these results are applied to an example model known as Brockett oscillator. Finally, using the Brockett oscillator as a common dynamics, output oscillatory synchronization results are given for heterogeneous nonlinear systems of relative degree 2 or higher. An application example of Brockett oscillator for power-grid synchronization is also presented. Some outlooks are provided regarding future research directions.     

Quasi‐synchronization of multilayer heterogeneous networks with a dynamic leader

This article considers the pinning quasi‐synchronization problem for a class of leader‐following multilayer heterogeneous complex networks. The leader has nonzero control inputs that are unavailable to the followers. Multilayer heterogeneous networks with heterogeneous node dynamics and two different layer structures are proposed in this article. Two types of discontinuous coupling laws are designed for achieving synchronization in multilayer heterogeneous networks. Based on Lyapunov stability theory and the matrix theory, some sufficient criteria for pinning quasi‐synchronization are derived, and the upper bound of quasi‐synchronization errors is solved. Finally, numerical simulations are performed to illustrate the effectiveness of the theoretical results.     

Dissipativity and synchronization of fractional-order output-coupled neural networks with multiple adaptive coupling weights

Different from the majority of existing results that focus on the passivity analysis of nonlinear systems, this paper attempts to analyze the more general QSR-dissipativity of fractional-order neural networks that own output coupling and multiple coupled weights, where outer coupling weights can be adjusted online by developing an adaptation law. Using the linear matrix inequality technique, several sufficient criteria that not only guarantee the QSR-dissipativity of the network system but also achieve global synchronization even under zero input are established. Of particular significance is the proposal of a fractional Lyapunov-like lemma, which plays a crucial role in verifying the asymptotic stability of synchronization errors. Finally, a simulation example is presented to verify the plausibility of the theoretical results.