Liu混沌系统的混沌分析及电路实验的研究

研究了一种新型混沌系统——Liu混沌系统的基本动力学行为以及电路实现的问题，给出了相图、庞卡莱映射、功率谱以及李雅普诺夫指数，基于李雅普诺夫指数谱和分叉图分析了系统参数对Liu混沌系统的影响.最后设计硬件电路证实了Liu混沌系统以及Liu混沌系统随系统参数变化时的各种状态的存在.给出数值仿真和电路实验的结果. 关键词： Liu混沌系统 分岔 电路实验     

Realization of fractional-order Liu chaotic system by circuit

In this paper, chaotic behaviours in the fractional-order Liu system are studied. Based on the approximation theory of fractional-order operator, circuits are designed to simulate the fractional- order Liu system with $q=0.1-0.9$ in a step of 0.1, and an experiment has demonstrated the 2.7-order Liu system. The simulation results prove that the chaos exists indeed in the fractional-order Liu system with an order as low as 0.3. The experimental results prove that the fractional-order chaotic system can be realized by using hardware devices, which lays the foundation for its practical applications.     

Liu混沌系统的线性反馈同步控制及电路实验的研究

研究了新型混沌系统——Liu混沌系统的同步控制问题，基于Liu混沌系统的混沌特性，采用线性反馈控制方法，给出了实现Liu混沌系统同步的控制参数取值范围，数值仿真和电路实验证实了该方法的有效性. 关键词： Liu混沌系统 线性反馈控制 混沌同步 电路     

Liu混沌系统的非线性反馈同步控制

研究了新型混沌系统——Liu系统的同步控制问题.基于Lyapunov稳定性理论，采用非线性反馈控制方法，给出了Liu系统实现自同步的充分条件以及控制律参数的取值范围；结合参数自适应控制方法，实现了Liu混沌系统与统一混沌系统的异结构系统快速同步.数值仿真证明了该方法的有效性. 关键词： Liu混沌系统 混沌同步 非线性反馈控制 参数自适应控制     

Realization of fractional-order Liu chaotic system by a new circuit unit

A new circuit unit for the analysis and the synthesis of the chaotic behaviours in a fractional-order Liu system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to describe the dynamic behaviours of the fractional-order Liu system with α = 0.9. The results between simulation and experiment are in good agreement with each other, thereby proving that the chaos exists indeed in the fractional-order Liu system.     

一类多翼蝴蝶混沌吸引子及其电路实现

提出了一种构造多翼蝴蝶混沌吸引子的新方法,在Liu混沌系统的基础上,通过设计一种新的分段线性函数,构造了一个产生多翼蝴蝶混沌吸引子的混沌系统,对系统的平衡点、Lyapunov指数谱、分岔图、相图、频谱和Poincare截面进行了分析。最后,设计了相应的硬件电路,电路实验结果与数值仿真结果一致,验证了该方法的可行性和有效性。     

分数阶Liu混沌系统及其电路实验的研究与控制

基于波特图的频域近似方法,研究了分数阶Liu混沌系统,并设计了一种树形电路单元来实现分数阶Liu混沌系统,通过对2.7阶Liu混沌系统的电路仿真和实验,以及α=0.8—0.1(步长0.1)Liu混沌系统的电路仿真,验证了树形电路单元的有效性,证实分数阶Liu混沌系统中确实存在混沌现象,且存在混沌的最低阶数为0.3. 设计简单有效的线性反馈控制器,实现了分数阶Liu混沌系统的混沌控制. 关键词： 分数阶Liu系统 电路实验 混沌控制     

一个新的混沌系统的构建与实现

参考Chen系统和Liu系统的构建模式, 对Lorenz系统进行改造, 构建一个新的三维自治混沌系统. 讨论了平衡点的性质, 给出了系统的功率谱图、 Poincare截面图, 并利用分岔图和Lyapunov指数谱详细分析了各参数变化对系统动力学行为的影响. 研究发现, 交叉乘积项参数d和平方项参数e变化时, 系统的Lyapunov指数谱保持恒定, 且参数d具有全局非线性调幅功能, 参数e具有局部非线性调幅功能. 另外, 设计了该混沌系统的模拟电路, 实验结果证实了混沌系统的可实现性.     

A novel hyperchaos evolved from three dimensional modified Lorenz chaotic system

This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.[第一段]     

类Liu系统在水声微弱信号检测中的应用研究

利用三阶混沌系统构造了一种新的微弱信号检测系统——类Liu系统, 对类Liu 系统进行了深度的理论分析. 类Liu系统中, 当输入待测信号幅值大于某临界值时, 系统可达到平衡点S₀, S₀中系统变量x平衡于摄动力信号, 系统变量y, z收敛于零态, 且S₀ 对应的Lyapunov指数小于零. 通过Matlab仿真、Multisim电路仿真以及实际电路证明了类Liu系统的周期态收敛性及广域检测性, 解决了传统Duffing系统进行微弱信号检测时周期态不收敛、只能进行窄域检测等问题, 同时谱级信噪比范围仍可达-46.57 dB. 类Liu系统采用了全新的设计理念, 具有较高的实用价值, 对未来海洋物联网中的水声通信有一定参考价值.     

一类四维多翼混沌系统及其电路实现

提出了一种产生多翼蝴蝶混沌吸引子的新方法.基于三维Lorenz系统,通过增加一个状态变量和一个分段线性函数,构造出一个四维多翼混沌系统.分析了系统的平衡点和Lyapunov指数谱.最后,设计出一个模拟电路,进行了电路实验.电路实验结果与数值仿真结果相一致,验证了该方法的可行性和有效性.     

一个新的四维混沌系统理论分析与电路实现

分析了一个新的复杂的四维混沌系统的基本特性，该系统每个方程中包含一个三次交叉乘积项，共有9个平衡点，它们相对于原点和坐标轴具有完美的对称性，并且相对于线性特性和不变流形具有很好的相似性.描述了两个同时共存的对称双翼吸引子.最后，设计了一个模拟电路来实现这个新的四维混沌系统，表明数值仿真和电路实现具有很好的一致性，同时说明在应用上由于频率不同导致的仿真与物理实现之间的重要区别. 关键词： 四维混沌系统 Lyapunov 指数 共存双翼吸引子 电路实现     

一个新的三维混沌系统的分析、电路实现及同步

中心流形理论提供了一个将高维系统降维研究的方法，应用该理论研究了一个新的混沌系统的基本特性，给出中心流形上流方程，分析这个新的混沌系统的叉式分岔.通过构建电路实现了该混沌系统,从而验证了系统的混沌行为，证实了混沌吸引子的存在.同时说明了由于电路信号频率与数值信号频率的不同所带来的数值仿真与物理实现之间在应用上有着重要区别.最后利用单变量反馈控制方法实现了新系统的同步控制，并给出了完整的同步实现电路. 关键词： 三维混沌系统 中心流形 电路实现 同步     

Circuitry implementation of a novel nonautonomous hyperchaotic Liu system based on sine input

Based on the three-dimensional Liu system with a nonlinear term of square, this paper appends a state variable to the system, and further adds a driving signal of the sine signal to construct a novel 4-demensional nonautonomous hyperchaotic Liu system. The appended variable is formed by the product of the nonlinear quadratic term of the original state variables and the driving signal. Through adjusting the frequency of the driving signal, the system can be controlled to show some different dynamic behaviors. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the novel systems are analyzed. Furthermore, the corresponding hardware circuits are implemented. Both the experimental results and the simulation results confirm that the method is feasible. The method, which adjusts the frequency of the input sine signal to control the system to show different dynamic behaviors, can make the dynamic property of the system become more complex, but easier to be controlled accurately as well.     

A new multi-scroll chaotic system

This paper proposes a new simple autonomous chaotic system which can generate multi-scroll chaotic attractors. The characteristic of this new multi-scroll chaotic system is that the 4n+2m+4-scroll chaotic attractors are generated easily with n and m varying under n \le m. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on EWB (Electronics Workbench).     

四阶Colpitts混沌振荡器

提出了一种新的四阶Colpitts混沌振荡器.理论设计与电路实验表明,在三阶Colpitts混沌振荡器中的电感两端并联一个电容器C₃,可构建出一种四阶Colpitts混沌振荡器.当C₃的取值变化时,电路的谐振频率随之改变,从而使该振荡器经过倍周期分岔进入混沌状态.对四阶Colpitts混沌振荡器的平衡点、分岔和李氏指数等基本动力学问题进行了分析.最后通过数值仿真和电路实验证实了这一方法的可行性. 关键词： 四阶Colpitts混沌振荡器 混沌吸引子 电路实现     

一个新的混沌系统的动力学分析及混沌控制

提出了一个新的混沌系统,研究了其基本动力学特性.设计了实现该系统的混沌电路,电路实验结果验证了系统的混沌行为.根据Lyapunov稳定性理论,采用自适应backstepping控制方法,把系统控制到一个有界点.数值仿真证明了该方法的有效性和可行性.     

Circuit realization of the fractional-order unified chaotic system

This paper studies the chaotic behaviours of the fractional-order unified chaotic system. Based on the approximation method in frequency domain, it proposes an electronic circuit model of tree shape to realize the fractional-order operator. According to the tree shape model, an electronic circuit is designed to realize the 2.7-order unified chaotic system. Numerical simulations and circuit experiments have verified the existence of chaos in the fraction-order unified system.     

Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control

Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.     

新三维混沌系统及其电路仿真实验

提出了一个混沌系统，并对该系统的基本动力学特性进行了深入研究.得到该系统的Lyapunov指数、Lyapunov维数，给出了Poincaré映射图以及时域图和相图. 运用电子工作平台EWB软件对实现该新混沌系统的振荡器电路进行了仿真实验. 经过数值仿真和电路系统仿真证实该系统与以往发现的混沌吸引子并不拓扑等价，属于新的混沌系统. 关键词： 混沌系统 动力学行为 电路实现