分数阶线性时滞微分系统的有限时间稳定性

该文研究了含有时滞的分数阶微分系统的有限时间稳定性问题.首先通过构造新的Lyapunov函数,利用线性矩阵不等式给出线性分数阶时滞微分系统的有限时间稳定性条件.其次,在状态反馈控制器的作用下,给出分数阶时滞微分闭环系统的有限时间稳定条件,同时给出了控制器的设计方法.最后,通过两个例子来说明所得理论结果的有效性.     

含有离散时滞及分布时滞分数阶神经网络的渐近稳定性分析

研究了含有离散时滞及分布时滞的分数阶神经网络在Caputo导数意义下的渐近稳定性问题.通过构造Lyapunov函数和利用分数阶Razumikhin定理给出了含有离散时滞和分布时滞的分数阶神经网络渐近稳定性的充分条件,并给出4个例子验证了定理条件的有效性.     

Caputo分数阶时滞细胞神经网络的稳定性分析

研究了一类Caputo分数阶时滞细胞神经网络模型的稳定性.通过利用分数阶微积分中的常数变分法,得到了Caputo分数阶时滞细胞神经网络解的差分形式,推导出模型的有界解和平衡点的存在性与唯一性,最后证明了神经网络的全局指数稳定性.     

具有时变时滞的非线性分数阶退化微分系统的有限时间稳定性

本文研究了一类具有时变时滞的非线性分数阶退化微分系统的有限时间稳定性问题.首先通过退化微分系统理论得到了系统正则无脉冲的充分性条件.在此基础上通过建立Lyapunov泛函,并利用广义Gronwall不等式和线性矩阵不等式方法给出了含有时变时滞因素的分数阶退化微分系统的有限时间稳定性判据.最后给出具体的算例验证了定理条件的有效性.     

分数阶变时滞Cohen-Grossberg型BAM神经网络全局Mittag-Leffler稳定

主要研究分数阶变时滞Cohen-Grossberg型BAM神经网络,利用分数阶微积分有关性质,定义Mittag-leffler函数和对时间区间的有效划分,借助微分中值定理和一些分析技巧,给出了判定其系统解全局Mittag-Leffler稳定性充分条件.最后,给出数值例子以验证理论结果的有效性.     

一类具分布时滞的分数阶模糊C-G神经网络模型平衡点的存在唯一性与有限时间稳定性

研究了一类分数阶模糊C-G神经网络模型。利用压缩映射原理,讨论了该系统平衡点的存在唯一性,结合分数阶微分方程的性质和不等式技巧,证明了该系统平衡点的有限时间稳定性,并给出一个实例说明结果的正确性。     

基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性

研究了分数阶复值神经网络的稳定性.针对一类基于忆阻的分数阶时滞复值神经网络,利用Caputo分数阶微分意义上Filippov解的概念, 研究其平衡点的存在性和唯一性.采用了将复值神经网络分离成实部和虚部的研究方法, 将实数域上的比较原理、不动点定理应用到稳定性分析中, 得到了模型平衡点存在性、唯一性和全局渐近稳定性的充分判据.数值仿真实例验证了获得结果的有效性.     

一类分数阶神经网络模型的稳定性与Hopf分支分析

分析了一类分数阶神经网络的稳定性与Hopf分支问题.基于分数阶稳定性判据,得到了分数阶神经网络模型局部渐近稳定的条件.并以q为分支参数,得到了分数阶系统产生Hopf的条件.最后数值仿真证明了我们的结论.     

具有阶段结构的时滞分数阶捕食者-食饵系统的稳定性分析

本文研究了具有阶段结构的时滞分数阶捕食者-食饵系统稳定性,给出了两类具有阶段结构的时滞分数阶捕食者-食饵系统,并详细的对这两类系统进行了稳定性分析,得到了平衡点的渐近稳定性条件和参数稳定区间.此外,给出了两个数值实验,证明了理论结果的有效性.     

一类基于忆阻器分数阶时滞神经网络的修正投影同步

基于忆阻器分数阶时滞神经网络的研究是一个热点问题.该文主要研究了基于忆阻器分数阶时滞混沌神经网络的修正投影同步.结合分数阶微分不等式,得到了实现主动-被动系统获得同步的充分条件.其研究结果更具有一般性.相应的数值模拟证实了方法的有效性.     

Function projective synchronization for fractional-order chaotic systems

This letter investigates the function projective synchronization between fractional-order chaotic systems. Based on the stability theory of fractional-order systems and tracking control, a controller for the synchronization of two fractional-order chaotic systems is designed. This technique is applied to achieve synchronization between the fractional-order Lorenz systems with different orders, and achieve synchronization between the fractional-order Lorenz system and fractional-order Chen system. The numerical simulations demonstrate the validity and feasibility of the proposed method.     

Achieving synchronization between the fractional-order hyperchaotic Novel and Chen systems via a new nonlinear control technique

In this work, we discuss the stability conditions for a nonlinear fractional-order hyperchaotic system. The fractional-order hyperchaotic Novel and Chen systems are introduced. The existence and uniqueness of solutions for two classes of fractional-order hyperchaotic Novel and Chen systems are investigated. On the basis of the stability conditions for nonlinear fractional-order hyperchaotic systems, we study synchronization between the proposed systems by using a new nonlinear control technique. The states of the fractional-order hyperchaotic Novel system are used to control the states of the fractional-order hyperchaotic Chen system. Numerical simulations are used to show the effectiveness of the proposed synchronization scheme.     

Design of sliding mode controller for a class of fractional-order chaotic systems

In this paper, a sliding mode control law is designed to control chaos in a class of fractional-order chaotic systems. A class of unknown fractional-order systems is introduced. Based on the sliding mode control method, the states of the fractional-order system have been stabled, even if the system with uncertainty is in the presence of external disturbance. In addition, chaos control is implemented in the fractional-order Chen system, the fractional-order Lorenz system, and the same to the fractional-order financial system by utilizing this method. Effectiveness of the proposed control scheme is illustrated through numerical simulations.     

Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller

This paper proposes a novel fractional-order sliding mode approach for stabilization and synchronization of a class of fractional-order chaotic systems. Based on the fractional calculus a stable integral type fractional-order sliding surface is introduced. Using the fractional Lyapunov stability theorem, a single sliding mode control law is proposed to ensure the existence of the sliding motion in finite time. The proposed control scheme is applied to stabilize/synchronize a class of fractional-order chaotic systems in the presence of model uncertainties and external disturbances. Some numerical simulations are performed to confirm the theoretical results of the paper. It is worth noticing that the proposed fractional-order sliding mode controller can be applied to control a broad range of fractional-order dynamical systems.     

Parameter identification and synchronization of fractional-order chaotic systems

The knowledge about parameters and order is very important for synchronization of fractional-order chaotic systems. In this article, identification of parameters and order of fractional-order chaotic systems is converted to an optimization problem. Particle swarm optimization algorithm is used to solve this optimization problem. Based on the above parameter identification, synchronization of the fractional-order Lorenz, Chen and a novel system (commensurate or incommensurate order) is derived using active control method. The new fractional-order chaotic system has four-scroll chaotic attractors. The existence and uniqueness of solutions for the new fractional-order system are also investigated theoretically. Simulation results signify the performance of the work.     

Chaos control and function projective synchronization of fractional-order systems through the backstepping method

We study the chaos control and the function projective synchronization of a fractional-order T-system and Lorenz chaotic system using the backstepping method. Based on stability theory, we consider the condition for the local stability of nonlinear three-dimensional commensurate fractional-order system. Using the feedback control method, we control the chaos in the considered fractional-order T-system. We simulate the function projective synchronization between the fractional-order T-system and Lorenz system numerically using MATLAB and depict the results with plots.     

超混沌分数阶Bao系统的自适应滑模同步控制

研究超混沌分数阶Bao系统自适应滑模同步,设计出分数阶滑模函数、适应规则和控制器,取得超混沌分数阶Bao系统自适应滑模同步的充分条件,文末用MATLAB数值仿真验证了所得结论.     

Some analytical and numerical investigation of a family of fractional-order Helmholtz equations in two space dimensions

In this article, we aim at solving a family of two-dimensional fractional-order Helmholtz equations by using the Laplace-Adomian Decomposition Method (LADM). The fractional-order derivatives, which we use in this investigation, follows the Liouville-Caputo definition. Our results based upon the LADM are obtained in series form that helps us in analyzing the analytical solutions of the fractional-order Helmholtz equations considered here. For illustration and verification of the analytical procedure using the LADM, several numerical examples and graphical representations are presented for the analytical solution of the fractional-order Helmholtz equations. The mathematical analytic procedure, which we have used here, has shown that the LADM is a fairly accurate and computable method for the solution of problems involving fractional-order Helmholtz equations in two dimensions. In an analogous manner, one can apply the LADM for finding the analytical solution of other classes of fractional-order partial differential equations.     

Estimation of domain of attraction for the fractional-order WPT system

This paper investigates the problem of domain of attraction of the fractional-order wireless power transfer (WPT) system. As a fractional-order piecewise affine system, firstly, the model of the fractional-order WPT system is established. Secondly, based on the Lyapunov function approach and the inductive method, sufficient conditions of the boundedness for the fractional-order WPT system and the fractional-order system with periodically intermittent control are derived, respectively. In the meantime, the relevant inequality technique is introduced so as to decrease the conservatism of the results. The derived results can be used for estimating the domain of attraction of the systems. Finally, several examples are given to demonstrate the obtained results. Simulation shows that the conservatism of the results is indeed reduced in theory, and the designed controller is effective.