| Complex dynamical networks widely exist in nature and all areas of human life,work and social interaction.Their potential applications range from all fields of engineering industry.The research on complex dynamical networks is of great significance.In reality,there may be many kinds of association relations between nodes in many networks,that is,the single link between nodes in complex dynamical networks can no longer satisfy the description of this complex multi-attribute node relationship.Such as a complex communication network including telephone,letters,Email and other means of communication;a logistics/passenger transport network including water transport,air transport,land transport and other different modes of transport etc.Therefore,as for the modeling of this kind of network,we should make full use of the idea of multi network forms fusion to construct a proper multi-links complex dynamical networks to describe and study.Artificial neural network is an important cross research branch of complex dynamical networks in the field of biological engineering.With the deep understanding of the biological nervous system,the researchers are not satisfied with the simulation of the synaptic function of the resistors in the artificial neural network.Therefore,combined with the latest research results of the important electronic components memristor,researchers have found that replacing resistor with memristor will make artificial neural networks better simulate the memory and learning functions of biological nervous system.Therefore,the memristor-based neural networks model has come into being and has received extensive attention and research.According to the research results of the real biological structure and working mechanism of neurons,neurons can have multiple connections at the same time to execute excitation conduction,and different connections can be different types of synapses.Therefore,in fact,the existing classical memristor-based neural networks model with single link is not enough to describe the complex system structure.So,based on the classical memristor-based neural network model,this paper improves it to modeling the multi-links memristor-based switching networks and study in depth.It is well known that network synchronization is a very important cluster dynamical behavior.Synchronization phenomenon has a profound influence on the real system’s work and production.It may promote the actual system’s work effect and performance,also may bring devastating calamity.Therefore,it is of great practical significance to study the synchronization behavior of the network system and to realize the favorable guidance of the control technology exploration.This paper studies various synchronization problems of different complex dynamical networks,and designs and implements appropriate controllers for different synchronization types to guide corresponding stability and synchronization goals.According to the different control conditions and theoretical results obtained by the study,we design the simulation experiment to verify their feasibility and effectiveness.This paper is divided into six chapters,which mainly deals with the stability and synchronization control of complex dynamical networks with multi-links and time-varying delays.The construction of networks environment is as close as possible to consider the real situation.The research on synchronization control strategies of multiple types of synchronization including asymptotic synchronization,exponential synchronization,finite time synchronization,fixed time synchronization have been studied,such as feedback control strategy,adaptive control strategy,control strategy,intermittent pinning control strategy.The main contents of this paper are divided into the following several aspects:1.The problem of finite-time/fixed-time synchronization for multi-links coupled complex dynamical networks is studied.Considering the real situation of the network,the connection in each sub-network of the multi-links complex dynamical networks adopts single propagation delay,which only considers the time varying delay of information passing from the other nodes to the current node.In this paper,two classes of feedback delay controllers with multi-links coupling are proposed,and the appropriate Lyapunov functions are designed to obtain the constraints and some effective criteria for fixed time synchronization and finite time synchronization of the drive-response network.The correctness and effectiveness of these theoretical results are verified by numerical simulation.2.Considering the characteristics of the memory and learning of memristor as well as the real structure and working mechanism of neurons in biological systems,this paper improves the classical memristor-based neural networks model to put forward the mathematical model of memristor-based switching networks(MSNs)with multi-links.In this work,we introduce impulsive perturbation factor and design a type of adaptive controller to discuss the finite time synchronization and asymptotic synchronization of the multi-link memristor-based switching networks under impulsive perturbation.The corresponding synchronization constraints and criteria are obtained.In addition,an adaptive controller based on the idea of intermittent control is designed to achieve finite-time synchronization and asymptotic synchronization under the premise of effective control cost compression.Some theoretical calculation formulas and synchronization criteria are obtained through synchronous control research.The results of the numerical simulation show that the theoretical results obtained in this paper are correct and effective.3.Considering the fact that the network system in practice is always faced with a variety of unsafety factors,the uniform random attacks are a kind of unsafety factor to be mainly considered in modeling the network environment.In the multi-links memristor-based switching networks,attacks and multiple time-varying delays are introduced.The stability and finite-time synchronization/exponential synchronization control strategy of the network are studied.In this paper,the suitable updating rule and effective adaptive controller are designed.Based on the proper Lyapunov function,we derive some effective criteria which can be used to ensure the network system to achieve finite-time synchronization or asymptotic synchronization under uniform random attacks.4.In this paper,a multi-links memristor-based switching networks which are closer to the construction and real working mechanism of neurons are modeled.The mixed delays term containing discrete delay and distributed delay is introduced into the model.In order to explore the problem of stability and synchronization of the network model,a hybrid control strategy integrating the idea of intermittent control and pinning control is designed,which also achieves the goal of reducing the control cost flexibly.Based on the key theory of differential inclusions,some effective control criteria to ensure asymptotic synchronization or exponential synchronization are obtained.And their feasibility and effectiveness are verified by numerical simulation. |
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