一类分数阶复杂网络混沌系统的投影同步

根据分数阶系统的相关理论研究了一类分数阶复杂网络混沌系统的投影同步问题,给出了分数阶复杂网络以及分数阶时滞复杂网络系统实现投影同步的充分性条件,仿真结果表明了方法的正确性.     

分数阶复杂网络的混合投影同步研究

主要针对一类节点为分数阶混沌系统的复杂网络混合投影同步进行研究.基于分数阶系统的稳定性理论和非线性反馈控制方法,通过设计有效的控制器,实现了不同节点的复杂网络的混合投影同步,并给出了实现投影同步的充分条件,不仅从理论上分析了该控制器可以使复杂网络系统实现投影同步,而且大量的数值模拟证明所设计控制器的正确性和有效性.     

两个具有耦合时滞的分数阶复杂网络的延迟投影同步与参数辨识

研究两个具有耦合时滞的分数阶复杂网络的延迟投影同步与参数辨识的问题.首先,建立具有耦合时滞以及模型参数不确定分数阶复杂网络模型,并给出驱动网络与响应网络的延迟投影同步误差模型;其次,设计有效的控制器以及参数自适应律以实现两个网络之间的延迟投影同步与参数辨识,给出了实现延迟投影同步与参数辨识的充分条件,对该充分条件给出了...     

分数阶Rayleigh--Duffing-like系统的自适应追踪广义投影同步

本文针对分数阶Rayleigh-Duffing—like系统，设计了控制器和未知参数的辨识规则，实现了含有未知参数和随机扰动的分数阶Rayleigh—Duffing—like系统同给定信号的广义投影同步．数值仿真表明了所设计的控制器及未知参数辨识规则的有效性．     

两个不同分数阶混沌系统的广义投影同步

针对不同的分数阶混沌系统的同步问题,基于分数阶微积分理论和分数阶线性系统稳定性理论,设计了相应的控制器,实现了分数阶Chen系统和Lorenz系统之间的广义投影同步,数值仿真的结果验证了该控制方法的有效性和可行性。     

一类异结构分数阶复杂网络的自适应同步

复杂网络结构的复杂性以及节点行为的多样性等因素, 使得分数阶复杂网络的同步与控制研究得到了国内外研究者的广泛关注。本文讨论了异结构分数阶复杂网络的同步问题。应用自适应控制方法设计出一类非常简单的控制器,基于分数阶稳定性理论,选择合适的分数阶参数,推导出两类异结构分数阶复杂网络状态同步的充分条件,仿真结果进一步验证了本文所设计自适应控制器的有效性,并详细分析了分数阶参数复杂网络同步的影响。     

两个分数阶混沌系统的广义投影同步及电路实现

研究了分数阶混沌系统的广义投影同步及电路实现。基于非线性观测器,提出了用于实现分数阶混沌系统的广义投影同步的一般方法。并建立了相关的数学模型,证明结果的有效性。运用了Matlab进行数字仿真进一步表明该方法的可行性。最后,利用Multisim设计模拟电路,其结果与Matlab的仿真结果吻合,为分数阶混沌系统同步今后的实际运用打下基础。     

基于非线性牵制控制的分数阶混沌网络聚同步

针对分数阶混沌复杂网络,提出一种非线性牵制控制策略实现网络聚同步.根据网络结点的不同属性,只对群间点施加非线性控制,然后基于分数阶系统稳定性理论,给出了实现聚同步的充分条件.数值仿真验证了该聚同步方案的有效性和正确性,同时深入讨论了控制增益和耦合强度等对聚同步的影响.     

基于自适应模糊滑模控制的分数阶混沌系统的投影同步

基于模糊控制理论和滑模控制理论以及自适应控制理论,研究了一类含有外部扰动的不确定分数阶混沌系统的混合投影同步问题.提出了一种自适应模糊滑模控制的分数阶混沌系统投影同步方法.模糊逻辑系统用来逼近未知的非线性函数和外部扰动,并且对逼近误差采用了自适应控制,同时构造了一种具有较强鲁棒性的分数阶积分滑模面.应用分数阶Barbalat引理设计了自适应模糊滑模控制器和参数自适应律.最后数值仿真结果验证了所提控制方法的有效性.     

一类分数阶四维混沌系统及其投影同步

提出了一个新的四维自治类新混沌系统.首先在整数阶下分析了该系统的基本动力学特性.并利用数值仿真、功率谱分析了当参数固定时,分数阶新混沌系统随微分算子阶数变化时的动力学特性.研究表明:当微分算子阶数为0.85时,分数阶新系统随参数变化经短暂混沌和边界转折点分叉而进入混沌.针对一类结构部分未知分数阶混沌系统,基于Cheby...     

Decentralized Adaptive Strategies for Synchronization of Fractional-order Complex Networks

This paper focuses on synchronization of fractionalorder complex dynamical networks with decentralized adaptive coupling. Based on local information among neighboring nodes, two fractional-order decentralized adaptive strategies are designed to tune all or only a small fraction of the coupling gains respectively. By constructing quadratic Lyapunov functions and utilizing fractional inequality techniques, Mittag-Leffler function, and Laplace transform, two sufficient conditions are derived for reaching network synchronization by using the proposed adaptive laws. Finally, two numerical examples are given to verify the theoretical results.      

Synchronization Criteria for Complex Dynamical Networks with State and Coupling Time‐Delays

This paper is concerned with the problem of synchronization of complex dynamical networks with state and coupling time‐delays. Therefore, larger class and more complicated complex dynamical networks could be considered for the synchronization problem. Based on the Lyapunov‐Krasovskii functional, some delay‐independent and delay‐dependent criteria are obtained and formulated in the form of linear matrix inequalities (LMIs) to ascertain the synchronization between each node of the complex dynamical network. The effectiveness of the proposed method is illustrated using some numerical simulations.     

Synchronization of Complex Dynamical Networks with Dynamical Behavior Links

In this paper, synchronization of a complex dynamical network (CDN) is investigated while the coupling connections of the network exhibit dynamic behavior. As it is shown in simulations, the dynamic links can cause synchronization losing in the network whereas the links in many real‐world CDNs have dynamic behavior. To analyzing the effect of these links, two different CDN models are considered: without time delays and with delays in the coupling connections. By means of Lyapunov(‐Krasovskii) theory, stability analysis of the error dynamics between the nodes of these CDNs and an introduced individual node is investigated which yields some conditions in the form of linear matrix inequalities (LMIs). These LMIs can be solved easily by various existing LMI solvers. Moreover, the gain matrices of state feedback controllers will be obtained by solving the LMIs. In the end, illustrative numerical examples are given to specify the effectiveness of the proposed method.     

Parameter Estimation and Topology Identification of Uncertain General Fractional-order Complex Dynamical Networks with Time Delay

Complex networks have attracted much attention from various fields of sciences and engineering in recent years. However, many complex networks have various uncertain information, such as unknown or uncertain system parameters and topological structure, which greatly affects the system dynamics. Thus, the parameter estimation and structure identification problem has theoretical and practical importance for uncertain complex dynamical networks. This paper investigates identification of unknown system parameters and network topologies in uncertain fractional-order complex network with time delays (including coupling delay and node delay). Based on the stability theorem of fractional-order differential system and the adaptive control technique, a novel and general method is proposed to address this challenge. Finally two representative examples are given to verify the effectiveness of the proposed approach.      

Finite‐Time Synchronization of General Complex Dynamical Networks

The main objective of the present paper is to further investigate finite‐time synchronization of a general complex dynamical network from the viewpoint of dynamics and control. By utilizing the finite‐time stability theory combined with the inequality techniques, several sufficient criteria on finite‐time synchronization are derived analytically. And some effects of control parameters on synchronization speed and synchronization time are also drawn. It is shown that control gains play an important role in making the dynamical networks finite‐time exponentially synchronized. Furthermore, the results are applied to a typical nearest‐neighbor coupled network composing of chaotic FitzHugh‐Nagumo (FHN) neuron oscillators, and numerical simulations are given to demonstrate the effectiveness of the proposed control methodology.     

Non‐Fragile Synchronization Control For Markovian Jumping Complex Dynamical Networks With Probabilistic Time‐Varying Coupling Delays

This paper studies the problem of non‐fragile synchronization control for Markovian jumping complex dynamical networks with probabilistic time‐varying coupling delays. By constructing a new Lyapunov–Krasovskii functional (LKF) and combining the reciprocal convex technique, sufficient conditions for the complex dynamical networks to be globally asymptotically synchronized in the mean square sense are derived. The probability distribution of the delays have been proposed and delay probability‐distribution‐dependent conditions are derived in the form of linear matrix inequalities (LMIs). The derived conditions depend not only on the size of the delay but also on the probability of the delay taking values in some intervals. Further, a non‐fragile synchronization controller is proposed. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.     

分数阶Rossler混沌系统的模糊同步控制

采用分数阶T-S模糊模型对分数阶Rossler混沌系统建模．使用并行分布式补偿方法设计模糊状态反馈控制器,使得闭环系统极点位于稳定区域内,从而保证闭环系统满足渐近稳定性条件．利用所设计的模糊状态反馈同步控制器实现了两个具有不同初始条件的分数阶Rossler混沌系统的同步．数值仿真结果表明该方案的有效性．     

两个异构复杂网络的广义同步与参数识别

本文实现复杂网络未知系统参数的识别.针对系统未知参数,提出基于广义同步（Generalized synchronization,GS）的参数识别方法.该方法基于Babalat引理,利用Lyapunov稳定性理论,构造另一个具有不同拓扑结构和动力学方程的网络,并设计有效的自适应控制器,实现具有耦合时滞两个不同网络的广义同步,同时准确识别未知参数.与基于完全同步的参数识别方法相比,该方法能够构造低维的系统去识别高维系统的参数.数值实验验证了算法的有效性.     

Pinning Synchronization Between Two General Fractional Complex Dynamical Networks With External Disturbances

In this paper, the pinning synchronization between two fractional complex dynamical networks with nonlinear coupling, time delays and external disturbances is investigated. A Lyapunov-like theorem for the fractional system with time delays is obtained. A class of novel controllers is designed for the pinning synchronization of fractional complex networks with disturbances. By using this technique, fractional calculus theory and linear matrix inequalities, all nodes of the fractional complex networks reach complete synchronization. In the above framework, the coupling-configuration matrix and the innercoupling matrix are not necessarily symmetric. All involved numerical simulations verify the effectiveness of the proposed scheme.