Hopf bifurcation analysis of a new modified hyperchaotic Lü system

The Hopf bifurcation of a new modified hyperchaotic Lü system with only one equilibrium is investigated in this paper. A detailed set of conditions are derived, which guarantee the existence of the Hopf bifurcation. Furthermore, by applying the normal form theory, the direction and type of the Hopf bifurcation, and the approximate expressions of bifurcating periodic solutions and their periods are determined. In addition, numerical simulation results supporting the theoretical analysis are given.     

Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system

A novel memristor-based multi-scroll hyperchaotic system is proposed. Based on a voltage-controlled memristor and a modulating sine nonlinear function, a novel method is proposed to generate the multi-scroll hyperchaotic attractors. Firstly, a multi-scroll chaotic system is constructed from a three-dimensional chaotic system by designing a modulating sine nonlinear function. Then, a voltage-controlled memristor is introduced into the above-designed multi-scroll chaotic system. Thus, a memristor-based multi-scroll hyperchaotic system is generated, and this hyperchaotic system can produce various coexisting hyperchaotic attractors with different topological structures. Moreover, different number of scrolls and different topological attractors can be obtained by varying the initial conditions of this system without changing the system parameters. The Lyapunov exponents, bifurcation diagrams and basins of attraction are given to analyze the dynamical characteristics of the multi-scroll hyperchaotic system. Besides, the field programmable gate array (FPGA) based digital implementation of the memristor-based multi-scroll hyperchaotic system is carried out. The experimental results of the FPGA-based digital circuit are displayed on the oscilloscope.     

On a new hyperchaotic system

A new hyperchaotic system is presented, which has two large positive and one small negative Lyapunov exponent over a large range of parameters. As a consequence, system orbits strongly expand in some directions but rapidly shrink in some other directions. These strong expansions and shrinking lead the system orbits to be more disordered and random. Bifurcation and Poincaré-map analyses further show that the system has very rich bifurcations in different directions and extremely complicated dynamics overall. Spectral analysis shows that the system in the hyperchaotic mode has an extremely broad frequency bandwidth of high magnitudes, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications.     

一个新的超混沌系统

基于一个新三维混沌系统,通过引入非线性控制器,构造出一个新的四维超混沌系统,并对该系统的动力学行为进行了研究,包括它的Lyapunov指数谱、分岔图等.分析表明,新的四维系统随着新引入的参数变化呈现周期、复杂周期、混沌及超混沌动力学行为;设计的硬件电路的实验结果也证实了相关结果. 关键词： 超混沌 Lyapunov指数 分岔图 混沌电路     

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.     

Implementation of a new memristor-based multiscroll hyperchaotic system

In this paper, a new type of flux-controlled memristor model with fifth-order flux polynomials is presented. An equivalent circuit which realizes the action of higher-order flux-controlled memristor is also proposed. We use the memristor model to establish a memristor-based four-dimensional (4D) chaotic system, which can generate three-scroll chaotic attractor. By adjusting the system parameters, the proposed chaotic system performs hyperchaos. Phase portraits, Lyapunov exponents, bifurcation diagram, equilibrium points and stability analysis have been used to research the basic dynamics of this chaotic system. The consistency of circuit implementation and numerical simulation verifies the effectiveness of the system design.     

基于FPGA视频合成系统设计与实现

为实现将输入的六路BT656视频无失真地合并成一路BT1120视频输出,采用将FPGA技术和视频合成系统相结合的设计方法,用verilog语言设计完成有效视频数据的抽取、SRAM乒乓操作以及FPGA对于视频的拼接处理方法。该系统由视频输入解码模块、存储模块、输出解码模块、i2c模块以及时钟管理模块组成。经算法仿真和逻辑综合,该设计可以实现视频合成的基本功能,满足视频监控系统的实时性要求.综合结果表明该设计占用FPGA片上逻辑资源少,系统运行频率高。     

Local bifurcation analysis of a four-dimensional hyperchaotic system

Local bifurcation phenomena in a four-dlmensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the bifurcation theory and the centre manifold theorem, and thus the conditions of the existence of pitchfork bifurcation and Hopf bifurcation are derived in detail. Numerical simulations are presented to verify the theoretical analysis, and they show some interesting dynamics, including stable periodic orbits emerging from the new fixed points generated by pitchfork bifurcation, coexistence of a stable limit cycle and a chaotic attractor, as well as chaos within quite a wide parameter region.     

A new hyperchaotic system and its linear feedback control

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies 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. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.     

基于DSP+FPGA的新型弹载计算机设计与实现

以某型号导弹飞行试验为研制背景,设计出一款精度高、通用性强的新型弹载计算机。该弹载计算机以高性能DSP和FPGA为系统框架,通过其丰富的外围接口和强大的处理能力,结合AD5764转换模块、MAX3490通信模块、ADUM1401四通道数字隔离器和ULN2801达林顿管驱动器组成的离散量输出等模块,解决了弹载计算机与弹上飞控部件之间复杂的并行数据处理以及多种控制算法实时解算问题,具有体积小、重量轻、精度高、实时性好等特点。经过多次飞行试验表明,该弹载计算机具有较高的可靠性和稳定性,应用前景非常广泛。     

四维切换超混沌系统

构建了一类关联且有多种切换方式的四维超混沌系统.依据系统的分岔图确定了各个子系统都处于混沌状态时，系统参数的取值范围.分析了这类四维超混沌系统平衡点的性质、超混沌吸引子的相图和Lyapunov指数等特性，设计了实现这类可切换超混沌系统的实际电路，利用系统选择器，一个电路可以实现四个关联子系统的功能. 关键词： 超混沌系统 分岔图 Lyapunov指数 切换     

基于FPGA的IRIG-B编解码设计与实现

随着系统间时间同步要求的提高,IRIG-B码被越来越多的应用于系统间的时统模块中;针对传统的单片机及专用芯片实现方法已经不能满足产品的可靠性和可移植性的问题,对基于FPGA的IRIG-B编解码设计和实现方法进行了研究;提出了一种将BCD码和二进制码之间相互转换的迭代算法;结合FPGA设计方法对IRIG-B编码和解码方法进行了研究;通过对实验方法进行仿真,结果表明该方法能够正确有效的对时间信息进行IRIG-B格式的解码和编码,并且FPGA内部的实现形式可以大大减少外部芯片及电路的使用,从而大幅提升产品的可靠性和可移植性。     

基于FPGA和ADS8638的数据采集系统的设计与实现

为了解决常用数据采集产品体积较大的问题,选用一种体积小,转换速度快的多通道AD转换芯片ADS8638,设计了FPGA与芯片间的接口电路,并采用verilog语言编写了控制程序,以控制ADS8638芯片对各通道输入的模拟量进行AD转换。通过软件仿真验证、静态时序分析,仿真和分析结果表明,该软件功能、性能、时序正确。最后,将软件经过综合、布局布线后下载到ACTEL FPGA芯片中进行硬件系统测试,测试结果表明,本技术方案设计合理,功能可靠,降低了常用数据采集系统的体积和功耗,具有良好的实用价值。     

Forming and implementing a hyperchaotic system with rich dynamics

A simple three-dimensional (3D) autonomous chaotic system is extended to four-dimensions so as to generate richer nonlinear dynamics. The new system not only inherits the dynamical characteristics of its parental 3D system but also exhibits many new and complex dynamics, including assembled 1-scroll, 2-scroll and 4-scroll attractors, as well as hyperchaotic attractors, by simply tuning a single system parameter. Lyapunov exponents and bifurcation diagrams are obtained via numerical simulations to further justify the existences of chaos and hyperchaos. Finally, an electronic circuit is constructed to implement the system, with experimental and simulation results presented and compared for demonstration and verification.     

Experimental robust synchronization of hyperchaotic circuits

Even if complete synchronization between two chaotic circuits can be reached only when the systems are identical, in this paper we address the robustness of synchronization in the presence of parameter mismatches between the coupled circuits in the case of hyperchaotic behavior. In particular, a master–slave scheme based on negative feedback [T. Kapitaniak, Synchronization of chaos using continuous control, Phys. Rev. E 50 (1994) 1642–1644] is considered and the strategy to design the slave system as an observer of the master is given. With the proposed approach, based on the concept of the Master Stability Function, the two circuits are coupled through a unique scalar signal. Experimental results obtained from two hyperchaotic circuits will be presented in order to show that synchronization occurs widely in the range of electronic component tolerances.     

The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system

This paper reports a new four-dimensional hyperchaotic system obtained by adding a controller to a three-dimensional autonomous chaotic system. The new system has two parameters, and each equation of the system has one quadratic cross-product term. Some basic properties of the new system are analysed. The different dynamic behaviours of the new system are studied when the system parameter $a$ or $b$ is varied. The system is hyperchaotic in several different regions of the parameter $b$. Especially, the two positive Lyapunov exponents are both larger, and the hyperchaotic region is also larger when this system is hyperchaotic in the case of varying $a$. The hyperchaotic system is analysed by Lyapunov-exponents spectrum, bifurcation diagrams and Poincar\'{e} sections.     

Control and synchronization of a hyperchaotic system based on passive control

In this paper, a new hyperchaotic system is proposed, and the basic properties of this system are analyzed by means of the equilibrium point, a Poincar map, the bifurcation diagram, and the Lyapunov exponents. Based on the passivity theory, the controllers are designed to achieve the new hyperchaotic system globally, asymptotically stabilized at the equilibrium point, and also realize the synchronization between the two hyperchaotic systems under different initial values respectively. Finally, the numerical simulation results show that the proposed control and synchronization schemes are effective.     

Controlling and synchronization of a hyperchaotic system based on passive control

In this paper, a new hyperchaotic system is proposed, and the basic properties of this system are analyzed by means of equilibrium point, Poincaré map, bifurcation diagram, and Lyapunov exponents. Based on the passivity theory, the controllers are designed to achieve the new hyperchaotic system globally, asymptotically stabilized at the equilibrium point, and also realize the synchronization between the two hyperchaotic systems under different initial values respectively. Finally, the numerical simulation results show that the proposed control and synchronization schemes are effective.     

A new Rosslor hyperchaotic system and its realization with systematic circuit parameter design

Based on two modified Rosslor hyperchaotic systems, which are derived from the chaotic Rosslor system by introducing a state feedback controller, this paper proposes a new switched Rosslor hyperchaotic system. The switched system contains two different hyperchaotic systems and can change its behaviour continuously from one to another via a switching function. On the other hand, it presents a systematic method for designing the circuit of realizing the proposed hyperchaotic system. In this design, circuit state equations are written in normalized dimensionless form by rescaling the time variable. Furthermore, an analogous circuit is designed by using the proposed method and built for verifying the new hyperchaos and the design method. Experimental results show a good agreement between numerical simulations and experimental results.     

Chaos-Based Lightweight Cryptographic Algorithm Design and FPGA Implementation

With the massive application of IoT and sensor technologies, the study of lightweight ciphers has become an important research topic. In this paper, an effective lightweight LZUC (lightweight Zu Chongzhi) cipher based on chaotic system is proposed to improve the traditional ZUC algorithm. In this method, a further algorithm is designed for the process of integrating chaos into the lightweighting of ZUC. For the first time, this design introduces the logistic chaotic system into both the LFSR (linear feedback shift register) and nonlinear F-function of the cryptographic algorithm. The improved LZUC algorithm not only achieves a certain effect in lightweighting, but also has good statistical properties and security of the output sequence. To verify the performance of the LZUC cipher, we performed NIST statistical tests and information entropy analysis on its output key streams and discussed the typical attacks on the algorithm’s resistance to weak key analysis, guess–determination analysis, time–stored data trade-off analysis, and algebraic analysis. In addition, we completed the design of an image security system using the LZUC cipher. Histogram analysis and correlation analysis are used to analyze both plaintext and ciphertext data. At the end of the article, the plaintext and ciphertext images displayed by LCD can be further visualized to verify the encryption effectiveness of the LZUC cipher.