Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench (EWB). Numerical simulations are presented to show these results.     

连续时间混沌系统的参数自适应同步

针对参数不一致系统以及同步无法实现的系统，基于误差渐进稳定收敛到零的原理，提出参数自适应加反馈同步法。数值模拟表明，通过选择合适的反馈系数，能够成功地实现混沌同步，并进一步将结果推广到超混沌系统。     

一种超混沌五阶自治电路的分析

在蔡式电路的L臂上增加一个RLC并联回路构造了一个超混沌五阶自治电路，对其进行数学建模和系统的理论分析，并结合数值仿真详细研究了其混沌动力学性态。通过对其相空间吸引子、庞卡莱映射、Lyapunov指数谱的分析表明，电路在参数值改变时，呈现出超混沌态、混沌态和周期态的振荡形式。最后对该电路从Hopf分叉变化到超混沌吸引子过程中的信号频谱进行了计算机模拟，估计其频谱分布范围并给出了电路的频谱分布特征。     

一种基于超混沌Mackey-Glass系统的语音加密算法

针对低维混沌序列加密语音信号保密性较差,而复合混沌序列加密信息又使得混沌系统难以用软硬件实现的问题,研究了一种基于参数辨识的超混沌时滞模型的加密算法.该算法引入了分块加密的思想,采用了一种映射的方法产生密钥,不仅实现简单,实用性强,而且有效地改善了由于计算机有限精度效应而产生的混沌周期行为,增强了保密性能.     

超混沌的同步化

提出了一种同步化超混沌系统的新方法。此法通过调节响应系统的参数来完成。参数的变化可用Routh-Hurwitz稳定性判据来确定。它是同步化的一般方法,并对外部噪声具有鲁棒性。     

On properties of hyperchaos: Case study

Some properties of hyperchaos are exploited by studying both uncoupled and coupled CML. In addition to usual properties of chaotic strange attractors, there are other interesting properties, such as: the number of unstable periodic points embedded in the strange attractor increases dramatically increasing and a large number of low-dimensional chaotic invariant sets are contained in the strange attractor. These properties may be useful for regarding the edge of chaos as the origin of complexity of dynamical systems. The project supported by the National Natural Science Foundation of China     

细胞神经网络超混沌系统同步及其在保密通信中的应用

本文研究四阶细胞神经网络超混沌系统同步方法,提出了一种基于细胞神经网络超混沌同步系统的扩展谱保密通信系统;这个保密通信系统不仅只需传递一个标量信号,而且由于采用了超混沌系统,所设计的保密通信系统具有更高的保密性。     

二阶级联声光双稳模型的动力学研究

本文构造了二阶级联声光双稳模型,计算了该系统Ｌｙａｐｕｎｏｖ指数的收敛行为,研究了系统的Ｌｙａｐｕｎｏｖ指数谱随各个参数的演化情况,作出了系统的分岔图和相空间图。分析结果表明,系统的变量结构对Ｌｙａｐｕｎｏｖ指数谱随参数的演化形式有重要的影响;系统随参数的变化由不动点经倍周期分岔直至进入混沌或超混沌。     

并联驱动声光双稳模型的超混沌控制

本文用变量反馈方法研究并联驱动声光双稳模型的超混沌控制,通过对系统的两个变量引直入相同形式的反馈项,在一定的反馈系数下,将系统的超混沌态的相空间进行了分割,压缩或控制到若干周期态,且系统各变量均可被控制到相同的周期数目。     

Analysis and implementation of a new hyperchaotic system

Based on a modified Lorenz system, a relatively simple four-dimensional continuous autonomous hyperchaotic system is proposed by introducing a state feedback controller. The system consists of four coupled first-order ordinary differential equations with three nonlinear cross-product terms. Some dynamical properties of this hyperchaotic system, including equlibria, stability, Lyapunov exponent spectrum and bifurcation, are analysed in detail. Moreover, an electronic circuit diagram is designed for demonstrating the existence of the hyperchaos, and verifying computer simulation results.