一类多涡卷Chua系统及其在图像加密中的应用

为使混沌序列表现出更复杂的特性,在典型的Chua系统上引入了分段线性函数,使所得的系统产生可控数量的多涡卷吸引子。对该系统进行动力学分析,分析结果表明,该系统混沌特性分布广泛,具有丰富的动力学行为。在此基础上,提出了一种基于Zigzag置乱和DNA编码的加密算法,并从多个方面对该算法的安全性进行了分析。仿真结果验证了该方法不仅能对图像进行有效加密,而且能有效抵抗各种常见的攻击,为图像加密提供了理论依据。

Design and implementation of a novel multi-scroll chaotic system

This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.

Implementation of a novel two-attractor grid multi-scroll chaotic system

This paper proposed a method of generating two attractors in a novel grid multi-scroll chaotic system. Based on a newly generated three-dimensional system, a two-attractor grid multi-scroll attractor system can be generated by adding two triangular waves and a sign function. Some basic dynamical properties, such as equilibrium points, bifurcations, and phase diagrams, were studied. Furthermore, the system was experimentally confirmed by an electronic circuit. The circuit simulation results and numerical simulation results verified the feasibility of this method.

MULTI-SCROLL HYPERCHAOTIC SYSTEM BASED ON COLPITTS MODEL AND ITS CIRCUIT IMPLEMENTATION

Based on the framework of Colpitts oscillator, a four-dimensional multi-scroll hyperchaotic system is proposed, which generates (2M+1)×(2N+1)-scroll chaotic and hyperchaotic attractors. The key strategy is to increase the number of index-2 equilibrium points by introducing two unit saw-tooth functions to extend and modify the Colpitts oscillator model. By using bifurcation diagram and phase portrait, the dynamical characteristics of the multi-scroll hyperchaotic system are briefly studied. Moreover, micro-controller based circuit realization is introduced and the experimental results dem-onstrate that 7×5-scroll chaotic and hyperchaotic attractors can be obtained in the digital circuit.

A new multi-scroll chaotic generator

In this paper a new simple multi-scroll chaotic generator is studied. The characteristic of this new multi-scroll chaotic generator is that it is easy to generate different number of scroll chaotic attractors through modifying the nature number n after fixing the suitable system parameters and it does not need complex mathematical derivation. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on Electronic Workbench （EWB）.

Adaptive generalized synchronization between Chen system and a multi-scroll chaotic system

Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is designed, by which the controlled Chen system can be synchronized with a multi-scroll chaotic system including unknown parameters. The Lyapunov direct method is exploited to prove that the synchronization error and parameter identification error both converge to zero. Numerical simulation results verify the feasibility of the proposed method further.

A novel multi-scroll chaotic generator:Analysis, simulation, and implementation

Based on a new three-dimensional autonomous linear system and designing a specific form of saturated function series and a sign function with two variables of system, which are employed to increase saddle-focus equilibrium points with index 2, a novel multi-scroll chaotic system is proposed and its typical dynamical characteristics including bifurcation diagram, Poincare map, and the stability of equilibrium points are analyzed. The hardware circuit is designed and the experimental results are presented for confirmation.

Multi-scroll hidden attractors and multi-wing hidden attractors in a 5-dimensional memristive system

A novel 5-dimensional（5D） memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincar′e map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.

A multi-directional controllable multi-scroll conservative chaos generator:Modelling,analysis,and FPGA implementation

Combing with the generalized Hamiltonian system theory,by introducing a special form of sinusoidal function,a class of n-dimensional(n=1,2,3)controllable multi-scroll conservative chaos with complicated dynamics is constructed.The dynamics characteristics including bifurcation behavior and coexistence of the system are analyzed in detail,the latter reveals abundant coexisting flows.Furthermore,the proposed system passes the NIST tests and has been implemented physically by FPGA.Compared to the multi-scroll dissipative chaos,the experimental portraits of the proposed system show better ergodicity,which have potential application value in secure communication and image encryption.

电容器耦合约瑟夫森结连接的Chua电路的同步控制

混沌现象是自然界中普遍存在的非线性动力系统的独特行为,具有不可预测、对初始条件敏感等特点,混沌同步在生物、医学和保密通信等领域有着广泛的应用。首先在Chua电路的基础上通过并联约瑟夫森结建立了一个四维的动力系统,并对其动力学行为进行了分析,结果表明该电路可以表现为周期态和混沌态。其次,结合数值模拟分类讨论了电容器耦合两个周期系统、两个混沌系统以及周期和混沌系统的完全同步行为,结果表明无论是否有外界磁场的作用。通过改变耦合强度的大小可以使电容器耦合的两个全同周期系统或两个全同混沌系统实现完全同步,而耦合两个参数不同的系统无法实现完全同步,但在合适的外界磁场下,可以达到几乎完全同步。

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 ＋ 2rn ＋ 4-scroll chaotic attractors are generated easily with n and m vaxying under n ≤ 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）.

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.

Novel two-directional grid multi-scroll chaotic attractors based on the Jerk system

A new method is presented to generate two-directional (2D) grid multi-scroll chaotic attractors via a specific form of the sine function and sign function series, which are applied to increase saddle points of index 2. The scroll number in the x-direction is modified easily through changing the thresholds of the specific form of the sine function, while the scroll number in the y-direction is controlled by the sign function series. Some basic dynamical properties, such as equilibrium points, bifurcation diagram, phase portraits, and Lyapunov exponents spectrum are studied. Furthermore, the electronic circuit of the system is designed and its simulation results are given by Multisim 10.

基于蔡氏混沌的隐性知识转移仿真研究

在知识经济时代,知识转移过程已成为管理学研究的热点问题。为分析隐性知识转移阻力变化对隐性知识转移过程及形态的影响,在梳理现有隐性知识转移文献的基础上,运用混沌理论构建蔡氏混沌隐性知识转移模型并进行仿真分析,研究隐性知识在主体间转移规律。研究结果表明:隐性知识转移具有初始状态敏感性等混沌特征,随着知识主体间合作与竞争平衡关系的变化,输出方转移意愿、输出方转移能力、接收方吸收动机、合作信任强度、互动交流程度也随之变化,隐性知识转移呈现出隐性知识转移全阻力类型、隐性知识转移高阻力类型、隐性知识转移中阻力类型、隐性知识转移低阻力类型以及隐性知识转移零阻力类型5种类型。基于仿真研究结果,提出隐性知识转移效果提升对策,同时,为隐性知识具有反馈机制的双向非线性转移过程研究提供新的量化方法和研究思路。

Chua’s系统的追踪控制与同步

为对Chua’s混沌系统进行控制,设计出一种含参控制器,使得受控系统的某一状态变量能追踪任意给定的参考信号,利用Lyapunov函数方法证明在此控制器作用下,该系统的状态变量按指数速率收敛到参考信号。在此基础上,研究受控Chua’s混沌系统的自同步和异结构同步问题,数值仿真结果说明了此控制器设计方法的有效性。

基于Chua电路混沌同步自保持特性的研究

本文介绍了Chua电路及其特性,给出实现非线性电阻的一种电路;利用Chua电路构造出一种驱动-响应混沌同步系统,利用仿真得出此同步系统具有一定鲁棒性、抗干扰等特性;根据此同步系统,仿真发现混沌同步具有自保持特性,并给出仿真结果,这一发现为混沌在保密通信的实际应用提供了依据。

分数阶Chua系统中的混沌现象及其同步控制

对分数阶Chua系统的混沌动力学行为做了更进一步的研究,研究发现Chua系统出现混沌的最低阶数仅为0.3,并算得此时系统的最大Lyapunov指数为0.016 4;其次,对分数阶Chua等一类具有一个标量非线性项的分数阶混沌系统给出控制策略,讨论了其观测器的设计问题,对该类分数阶混沌系统,给出了一个合适的控制器U,在此控制输入下仅利用一个非线性标量信号实施反馈就可以使观测器的状态变量与被观测分数阶混沌系统的状态变量达到同步。理论分析及仿真结果都证明了该同步方案的有效性。

利用模拟电感改进Chua电路的研究

首先介绍了Chua电路及其特性,给出实现非线性电阻的一种电路;然后设计了一种用集成运放、线性电阻和电容组成的模拟电感电路,利用模拟电感对Chua电路进行改进,取得了良好的效果;并且利用改进后的Chua电路构成的驱动-响应式混沌同步系统具有一定的鲁棒性、抗干扰等特性,为混沌在保密通信的实际应用奠定了基础。

多涡卷Chua混沌吸引子的设计与性能分析

为了设计结构复杂、性能优越的多涡卷混沌系统,采用理论分析和数值仿真的方法,通过设计一个连续非线性函数,建立了三阶Chua系统的单方向与网格多涡卷吸引子模型.在Matlab平台上,通过吸引子相图、最大Lyapunov指数、分岔图和Poincaré截面等方法,分析了多涡卷Chua混沌系统的动力学特性.研究结果表明,多涡卷Chua混沌吸引子具有丰富的动力学特性,仿真结果与理论分析一致,表明了多涡卷Chua混沌系统设计方法的有效性和设计模型的正确性.

变形Chua混沌系统及其同步问题的研究

混沌系统及其同步是混沌保密通信中的关键问题。提出了一种基于双曲正切非线性函数的变形Chua电路,分析了参数在不同取值时系统的吸引子特性,讨论了该系统的功率谱密度特性、分岔特性和旁加莱映射,并通过线性状态反馈实现了两个变形Chua系统的同步。不仅如此,还通过调整非线性函数,将该系统进一步拓展,产生了更复杂的多涡卷混沌吸引子,以更利于实际应用。仿真结果表明了本方法的有效性。