分数阶系统有限时间稳定性理论及分数阶超混沌Lorenz系统有限时间同步

研究了分数阶系统有限时间稳定性理论及分数阶混沌系统的同步问题.根据分数阶微分性质及分数阶系统稳定性理论,建立了分数阶系统有限时间稳定性理论并进行了证明.根据该理论设计控制器实现了分数阶超混沌Lorenz系统有限时间同步并运用数值仿真进行了验证. 关键词： 分数阶 超混沌Lorenz系统 稳定 有限时间同步     

一类分数阶混沌系统的自适应同步

针对一类分数阶混沌系统的同步问题,基于分数阶系统的类Lyapunov稳定性理论,设计了一种新的自适应同步控制器以及控制增益系数自适应律.与现有结果相比,该方法具有控制器结构简单、控制代价小以及通用性强等特点,可适用于大部分典型的分数阶混沌系统.最后,数值仿真结果验证了所提方法运用于分数阶混沌系统同步研究的有效性.     

一种分数阶混沌系统同步的自适应滑模控制器设计

针对分数阶混沌系统的同步问题, 基于滑模控制理论和自适应控制理论, 设计了一个具有较强鲁棒性的分数阶积分滑模面, 并提出了一种自适应滑模控制器在不消除非线性项的情况下实现一类三维分数阶混沌系统同步的方法. 利用所设计的自适应滑膜控制器实现了分数阶Chen系统、分数阶Liu系统以及分数阶Arneodo系统的混沌同步. 数值模拟仿真结果验证了所设计的控制器的有效性和可行性.     

分数阶混沌系统与整数阶混沌系统之间的同步

基于追踪控制的思想,利用分数阶系统稳定性理论,实现了分数阶混沌系统与整数阶混沌系统之间的混沌同步,给出了补偿器和反馈控制器的选择方法.以三维分数阶Chen系统和三维整数阶Lorenz混沌系统之间的混沌同步为例进行了数值仿真和电路仿真.研究表明了该同步方法的有效性。     

基于区间系统理论的分数阶混沌系统同步

通过设计一个非线性反馈控制器,实现了分数阶混沌系统的同步.与其他的分数阶混沌系统同步方法相比,提出的控制器设计方法保留了部分误差系统中的非线性项,而没有完全抵消同步误差系统的非线性项,有效改善了误差系统的控制性能.同时,应用区间分数阶线性时不变系统稳定性原理和线性矩阵不等式技术,得到了一个新的分数阶混沌系统同步的充分条件,进而获得的控制器保证了混沌系统同步.仿真结果验证了提出方法的有效性. 关键词： 区间分数阶时不变系统 分数阶混沌系统 混沌同步     

阶次不等的分数阶混沌系统同步

针对阶次不等的分数阶混沌系统同步问题,提出了一种将不等阶分数阶系统转化为等阶系统的方法,将不等阶分数阶系统的同步问题转化为等阶的异结构同步问题.利用该方法实现了阶次不等的分数阶Lorenz混沌系统的同步,数值仿真结果验证了该理论的正确性. 关键词： 不等阶 分数阶混沌系统 同步 异结构     

分数阶统一混沌系统的自适应同步

提出了分数阶统一混沌系统的自适应同步方法, 给出了自适应同步控制器和参数自适应率. 设计的单一控制器简单且只含有一个驱动变量. 所用同步方法适用于一类分数阶混沌系统的同步, 且具有较强的抗噪声能力, 具有较高的实用价值. 数值模拟结果表明了该方法的有效性. 关键词： 分数阶 统一混沌系统 自适应同步     

一个分数阶新超混沌系统的同步

研究了分数阶混沌系统的同步问题,以分数阶新超混沌系统为例,设计了三种同步方法,运用拉普拉斯变换理论和分数阶线性稳定理论给以证明,数值仿真或电路仿真证实了所提同步方法的有效性和可行性. 关键词： 分数阶 混沌同步 新超混沌系统     

一个新分数阶超混沌系统及其混沌同步

给出了一个新的分数阶超混沌系统,利用严格数学理论实现了该分数阶超混沌系统的混沌同步,在同步过程中并未删除响应系统的非线性项,理论分析与仿真计算表明了同步方法的有效性. 关键词： 分数阶超混沌系统 混沌同步 非线性项     

间歇同步分数阶统一混沌系统

根据分数阶微分方程的性质,研究了间歇控制分数阶系统的稳定性,提出了间歇控制分数阶系统的一般理论并给出了数学证明. 根据该理论设计控制器实现了分数阶统一混沌系统的间歇同步, 数值仿真验证了该理论的正确性. 关键词： 分数阶 统一混沌系统 间歇同步 稳定性     

Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors

A five-value memristor model is proposed, it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current. Then, based on the classical Liu–Chen system, a new memristor-based four-dimensional(4D) chaotic system is designed by using the five-value memristor. The trajectory phase diagram, Poincare mapping, bifurcation diagram, and Lyapunov exponent spectrum are drawn by numerical simulation. It is found that, in addition to the general chaos characteristics, the system has some special phenomena, such as hidden homogenous multistabilities, hidden heterogeneous multistabilities, and hidden super-multistabilities. Finally, according to the dimensionless equation of the system, the circuit model of the system is built and simulated. The results are consistent with the numerical simulation results, which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.     

Function projective lag synchronization of fractional-order chaotic systems

Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.     

One to four-wing chaotic attractors coined from a novel 3D fractional-order chaotic system with complex dynamics

A novel 3D fractional-order chaotic system is proposed in this paper. And the system equations consist of nine terms including four nonlinearities. It's interesting to see that this new fractional-order chaotic system can generate one-wing, two-wing, three-wing and four-wing attractors by merely varying a single parameter. Moreover, various coexisting attractors with respect to same system parameters and different initial values and the phenomenon of transient chaos are observed in this new system. The complex dynamical properties of the presented fractional-order systems are investigated by means of theoretical analysis and numerical simulations including phase portraits, equilibrium stability, bifurcation diagram and Lyapunov exponents, chaos diagram, and so on. Furthermore, the corresponding implementation circuit is designed. The Multisim simulations and the hardware experimental results are well in accordance with numerical simulations of the same system on the Matlab platform, which verifies the correctness and feasibility of this new fractional-order chaotic system.     

Generalized projective synchronization of the fractional-order chaotic system using adaptive fuzzy sliding mode control

An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractionalorder chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can be adaptively adjusted according to the external disturbances. Based on the Lyapunov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simulations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover,it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication.     

耦合分数阶混沌振荡器的主-从同步

近年来对分数阶系统的动力学研究得到了较为广泛的关注。本文研究了基于主-从耦合同步法的同步技术并实现了两个耦合的分数阶振荡器的混沌同步。仿真结果表明：在适当的耦合强度的调节下，该方法可实现两个耦合分数阶混沌振荡器的准确同步，且分数阶混沌振荡器的同步率明显慢于整数阶混沌振荡器的同步率；而耦合分数阶混沌振荡器在实现同步的过程中，随着阶数的提高，同步误差曲线变得平滑，这表明，系统阶数的提高改善了耦合混沌振荡器实现同步的平稳性。     

基于非线性观测器的一类分数阶混沌系统完全状态投影同步

基于分数阶系统稳定性理论,提出了用状态观测器来实现分数阶混沌系统完全状态投影同步的思想. 设计的状态观测器能够实现一类非线性分数阶系统的完全状态投影同步而不要求分数阶混沌系统是部分线性的,推广了投影同步的应用范围,且无需计算系统的条件Lyapunov指数. 另外,该方法理论严格,设计简单,能够达到任意比例因子的完全状态同步. 最后,利用该方法实现了分数阶Rssler系统的完全状态投影同步,数值仿真结果证实了它的有效性. 关键词： 分数阶 混沌系统 状态观测器 投影同步     

分数阶电子振荡器的混沌及其控制

本文研究了分数阶混沌电子振荡器的混沌行为。研究表明：混沌存在于阶数低于3阶的分数阶电子振荡器中，为了说明混沌行为的连续性，本文对分数阶电子振荡器进行了降阶、升阶 （2.8—3.2阶）的仿真分析。最后，本文基于自适应Backstepping法研究了分数阶电子振荡器的混沌控制，仿真结果表明了该方法的有效性和可行性。     

Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization

Based on the stability theory of the fractional order system,the dynamic behaviours of a new fractional order system are investigated theoretically.The lowest order we found to have chaos in the new three-dimensional system is 2.46,and the period routes to chaos in the new fractional order system are also found.The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent.Furthermore,a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system,and its validity is proved by Laplace transformation theory.     

Passive control of chaotic system with multiple strange attractors

In this paper we present a new simple controller for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form. Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one, and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.     

Synchronization in a unified fractional-order chaotic system

In this paper, the synchronization in a unified fractional-order chaotic system is investigated by two methods. One is the frequency-domain method that is analysed by using the Laplace transform theory. The other is the time-domain method that is analysed by using the Lyapunov stability theory. Finally, the numerical simulations are used to illustrate the effectiveness of the proposed synchronization methods.