Study Of Chaos Synchronization And Complex Networks Pingning Control

Nonlinear dynamics system and complex networks are two brilliant aspects of complexity science.Chaos is a special moving form of nonlinear dynamics system, whose trajectory of the orbits in the phase plane is very complex,pseudorandom,and can be observed in fairly simple dynamical systems.In modem science and technology,chaos is very important especially in studying complex systems.Complex networks are everywhere,ranging from nature and biological system to society.With the increasing of the networks complexity,how to control the whole network is an interesting topic.Pinning control is one of effective method in controlling networks with large inter-connection chaos nodes.By applying an action on some nodes,we can get the synchronization of the whole networks.This paper studies synchronization of nonlinear chaotic systems and pinning control of complex networks.The thesis contains the following(1)Develop a general chaotic system model and investigate the corresponding synchronization method. Considering the unknown system parameters,time-delay,different order and stochastic perturbation,we design an appropriative control method and realize general projective synchronization and hybrid projective synchronization.(2)Analyze the application of lag synchronization of chaotic systems with noise perturbation in secure communication.(3)Analyze the effects of degree correlation on the controllability of complex networks.The main contents can be summarized as follows:(1)Lag synchronization of a class of chaotic systems with unknown parametersIn real systems,the connection weights of the neurons depend on certain resistance and capacitance values which include uncertainties.On the other hand,the information storage and neurotransmission frequently suffer from the fluctuations. Therefore,when designing a chaos model,the parameter uncertainties and time-delay should be involved.By constructing a general chaos model and designing a proper nonlinear controller,lag synchronization is achieved.Also an appropriative Lyapunov function is established to verify the systems stability.Moreover,we illustrate the application of the proposed scheme by numerical simulation,which demonstrates the effectiveness and feasibility of the proposed synchronization method. (2)Hybrid projective synchronization of chaotic systems with different-orderThere is increasing interest in the study of chaotic synchronization with different structure and different order due to its wide existence in biological science and social science.One instance is the synchronization that occurs between heart and lung, where one can observe that circulatory and respiratory systems synchronize with different models and different order.In this paper,hybrid projective synchronization of chaotic systems is introduced.Reduced order projective synchronization and increased order projective synchronization of different chaotic systems with fully unknown parameters are considered in detail.By combining the adaptive control method and feedback control technique,the suitable controllers and parameters update laws are derived to achieve synchronization of chaotic systems.(3)Generalized projective stochastic perturbation synchronization of chaotic systemsIt is found that noise plays a significant role in chaotic synchronization.We investigate the generalized projective stochastic perturbation synchronization,where the drive and response systems are synchronized up to a scaling factor,which is a constant.We present general methods for achieving the projective synchronization of two chaotic systems with uncertain parameters.The conclusions are proved by Lyapunov stability theory.Moreover,the unknown parameters can be efficiently estimated according to a rigorous and systematic scheme.Finally,the corresponding simulation results are given to verify the effectiveness of the proposed methods.(4)Application of lag synchronization of chaotic systems with noise perturbation in secure communicationAs a special moving form of nonlinear dynamics system,chaos is a behavior of uncorrelated,board-band,noise-like and sensitivity to chaotic system initial conditions.Chaotic signal has the properties of ergodicity,aperiodic,determinate and random-like.These properties make the signal be fit for applying in secure communication and information encrypting.This paper researches the application of chaotic synchronization in secure communication.Based on the lag synchronization methods,the simulations of chaos masking and chaos parameter modulation are present.In the chaos masking secure communication scheme,some function are used to transform the useful signal,it will increase the difficulty of decryption.(5)Effects of degree correlation on the controllability of complex networksIn real world,complex networks have different degree-mixing patterns:many social networks are usually assortative mixing where nodes with similar degrees are tending to interconnect with each other.However,a lot of technological and biological networks are mixed disassortatively,nodes with large degrees are willing to select small-degrees ones as their neighbors.Pinning control is a feedback control action to reach the extended networks synchronization.Through the Master Stability Function (MSF) theory,the network controllability can be estimated in terms of the stability of this synchronous state of the extended network.Random pinning and max-degree pinning strategies are presented to control the networks.Mix-degree pinning scheme is firstly introduced and applied,in which some nodes are selected by sorted degrees, and others are selected randomly.It is found that disassortative mixing feature enhances the network controllability contrast to assortative mixing,to which the network controllability is sensible.