Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance

Based on fractional-order Lyapunov stability theory, this paper provides a novel method to achieve robust modified projective synchronization of two uncertain fractional-order chaotic systems with external disturbance. Simulation of the fractional-order Lorenz chaotic system and fractional-order Chen＇s chaotic system with both parameters uncertainty and external disturbance show the applicability and the efficiency of the proposed scheme.

Permutation-substitution image encryption scheme based on a modified chaotic map in transform domain

A new chaotic image encryption scheme based on permutation and substitution in the Fourier domain is presented.Fractional Fourier Transform(FRFT)is used before the encryption scheme to get a large degree of randomization.The permutation is achieved by Baker map and the substitution by a key-related-to-plain-image algorithm based on the modified Logistic map.Modification of the Logistic map is developed to increase the space of the encryption key,and hence increase the security.The key of the encryption algorithm dependents on the plain image,and thus,the cipher image is sensitive to both the initial key and the plain image to resist known-plaintext and chosen plaintext attacks.The key space is large and hence the algorithm can effectively resist brute-force attacks.The proposed scheme is examined using different performance evaluation metrics and the results prove that the proposed scheme is highly secure,and it can effectively resist different attacks.

Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems

We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory, the fractional order differential inequality, and the adaptive strategy. This synchronization approach is simple, universal, and theoretically rigorous. It enables the synchronization of O fractional-order chaotic systems to be achieved in a systematic way. The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.

Modified Logistic Maps for Cryptographic Application

In this paper, definition and properties of logistic map along with orbit and bifurcation diagrams, Lyapunov exponent, and its histogram are considered. In order to expand chaotic region of Logistic map and make it suitable for cryptography, two modified versions of Logistic map are proposed. In the First Modification of Logistic map (FML), vertical symmetry and transformation to the right are used. In the Second Modification of Logistic (SML) map, vertical and horizontal symmetry and transformation to the right are used. Sensitivity of FML to initial condition is less and sensitivity of SML map to initial condition is more than the others. The total chaotic range of SML is more than others. Histograms of Logistic map and SML map are identical. Chaotic range of SML map is fivefold of chaotic range of Logistic map. This property gave more key space for cryptographic purposes.

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.

一类含常数项的混沌系统在未知参数下的同步

研究了一个新的含有常数项的混沌系统在参数未知情况下的修正函数投影同步问题。对新的含有常数项的混沌系统从平衡点的稳定性、耗散性、poincare映射、功率谱及初值敏感性5个方面进行了特性分析。基于修正函数投影同步方法,设计了有效的控制输入及参数自适应律,根据Lyapunov函数稳定性定理从理论上证明修正函数投影同步误差系统在原点的渐近稳定性,从而实现了新混沌系统的修正函数投影同步控制。数值模拟仿真证明了同步方法的正确性,该同步方法可以应用于混沌保密通信的研究中。

A Modified Oppositional Chaotic Local Search Strategy Based Aquila Optimizer to Design an Effective Controller for Vehicle Cruise Control System

In this work,we propose a real proportional-integral-derivative plus second-order derivative(PIDD2)controller as an efficient controller for vehicle cruise control systems to address the challenging issues related to efficient operation.In this regard,this paper is the first report in the literature demonstrating the implementation of a real PIDD2 controller for controlling the respective system.We construct a novel and efficient metaheuristic algorithm by improving the performance of the Aquila Optimizer via chaotic local search and modified opposition-based learning strategies and use it as an excellently performing tuning mechanism.We also propose a simple yet effective objective function to increase the performance of the proposed algorithm(CmOBL-AO)to adjust the real PIDD2 controller's parameters effectively.We show the CmOBL-AO algorithm to perform better than the differential evolution algorithm,gravitational search algorithm,African vultures optimization,and the Aquila Optimizer using well-known unimodal,multimodal benchmark functions.CEC2019 test suite is also used to perform ablation experiments to reveal the separate contributions of chaotic local search and modified opposition-based learning strategies to the CmOBL-AO algorithm.For the vehicle cruise control system,we confirm the more excellent performance of the proposed method against particle swarm,gray wolf,salp swarm,and original Aquila optimizers using statistical,Wilcoxon signed-rank,time response,robustness,and disturbance rejection analyses.We also use fourteen reported methods in the literature for the vehicle cruise control system to further verify the more promising performance of the CmOBL-AO-based real PIDD2 controller from a wider perspective.The excellent performance of the proposed method is also illustrated through different quality indicators and different operating speeds.Lastly,we also demonstrate the good performing capability of the CmOBL-AO algorithm for real traffic cases.We show the CmOBL-AO-based real PIDD2 controller as the most efficient method to control a vehicle cruise control system.

Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.

A New Chaotic Function and Its Cryptographic Usage

Wheeler pointed ouuailat the period of Matthews＇ chaotic function （MCF） is often too short to be suitable for crypto- graphic usage in the manner of computer statistics, but this statement was given only through digital computation. In this paper, we proved by theoretical and practical method that period exists in MCF and analyzed the underlying reason. With two chaotic functions working together we presented a modified MCF （MMCF） that is non-periodic. The simulation tests with reconstruction of phase space showed that our modified MCF is of no period. And we described how to implement a cryptographic usage with MMCF.

Modified chaotic ant swarm to function optimization

The chaotic ant swarm algorithm （CAS） is an optimization algorithm based on swarm intelligence theory, and it is inspired by the chaotic and self-organizing behavior of the ants in nature. Based on the analysis of the properties of the CAS, this article proposes a variation on the CAS called the modified chaotic ant swarm （MCAS）, which employs two novel strategies to significantly improve the performance of the original algorithm. This is achieved by restricting the variables to search ranges and making the global best ant to learn from different ants＇ best information in the end. The simulation of the MCAS on five benchmark functions shows that the MCAS improves the precision of the solution.

Modified Projective Synchronization of Fractional-order Chaotic Systems with Different Dimensions

In this paper,the modified projective synchronization between two fractional-order chaotic systems with different dimensions is investigated.The added-order scheme and the reduced-order scheme are proposed,respectively.Based on the Laplace transformation and feedback control theory,controllers are designed such that two chaotic systems with different dimensions could be synchronized asymptotically under the presented schemes.Corresponding numerical simulations are given to show the effectiveness of the proposed schemes.

Complex Modified Projective Synchronization for Fractional-order Chaotic Complex Systems

The aim of this paper is to study complex modified projective synchronization（CMPS） between fractional-order chaotic nonlinear systems with incommensurate orders. Based on the stability theory of incommensurate fractional-order systems and active control method, control laws are derived to achieve CMPS in three situations including fractional-order complex Lorenz system driving fractional-order complex Chen system, fractional-order real Rssler system driving fractional-order complex Chen system, and fractionalorder complex Lorenz system driving fractional-order real Lü system. Numerical simulations confirm the validity and feasibility of the analytical method.

基于混沌理论的身份认证机制及其安全性分析

对挑战 /应答 (Challenge/Response)的认证机制进行了分析 ,指出其存在的缺点 ,并在此基础上 ,提出了改进方法 .给出了本地客户端静态密码和网络传输登录密码相结合的认证方式 .并利用混沌动力学方程生成混沌序列作为用户登录唯一身份标识 ,具有防窃听、防口令重放、防口令字典攻击等安全机制 ,减少登录认证交互次数 .

基于超混沌的保密通信系统

建立一种基于变型蔡氏电路的超混沌语音保密通信方案。在发端 ,利用变型蔡氏电路对发送信号进行调制 ,在收端对其进行逆变换解调出原信号。根据单向耦合法实现收发系统之间的同步 ,分析了同步的收敛特性。在此基础上设计硬件实验电路 ,进行传送语音信号的硬件实验研究 ,给出了实验结果。

基于变形蔡氏电路的混沌掩盖保密通信研究

用实际元器件做出了变形蔡氏电路,并把该电路应用于混沌掩盖保密通信中。分别给出了该电路用于混沌掩盖保密通信的仿真结果和实验结果,并对结果进行了分析。

扁球薄壳在大挠度下的动力学行为

根据薄壳非线性动力学理论,由扁球薄壳大挠度基本方程,在周边固定夹紧的条件下,用修正迭代法求出二次近似解析解,把大挠度解作为扁球薄壳的初挠度处理,推导出扁球薄壳在大挠度下的非线性动力学基本方程。利用扁球面壳的非线性动力学变分方程和协调方程,在夹紧固定的边界条件下,用Galerkin方法得到一个含二次、三次项非线性受迫振动微分方程.通过求Melnikov函数,给出可能发生混沌运动的条件.通过数字仿真绘出平面相图,证实混沌运动的存在.

四维混沌系统的自适应修正函数投影同步

研究了具有未知参数四维混沌系统的修正函数投影同步问题。基于Lyapunov稳定性理论、Barbalat引理和主动控制方法,设计自适应控制器和参数更新规则,实现了该类混沌系统的修正函数投影同步。同时,将该方法用于混沌掩盖保密通信。数值仿真表明了该方法可渐近实现函数投影同步,且在保密通信中可有效恢复信息信号。

基于改进混沌扩频序列的多用户混沌扩频通信系统的研究与仿真

提出一种改进混沌扩频序列,并将其应用在多用户混沌扩频通信系统中,给出了多用户混沌扩频通信系统的理论推导和SIMULINK仿真模型。对该系统进行了详细的性能分析,包括信噪比、用户数、改进混沌扩频序列的分形参数和初始值等各自对系统误码率的影响,并比较了改进混沌扩频序列与传统混沌扩频序列的系统误码率随信噪比和用户数的变化情况。结果表明改进混沌扩频序列要好于传统混沌扩频序列的系统误码率,具有较好的抗噪声和抗多址干扰的能力。

基于CCPSO及PP模型的洪灾评估方法及其仿真应用

以求解洪水灾情评估问题为背景,针对洪灾评估模型参数难以优化这一问题,研究了一种混沌文化粒子群算法(CCPSO)。该算法将PSO纳入文化算法的框架,并在算法中引入局部遍历搜索性能较强的混沌搜索,组成基于PSO的群体空间以及基于混沌优化的信念空间,通过两个种群的独立演化及信息交流来提升算法的全局寻优能力。典型的测试函数的测试结果表明,CCPSO可以有效克服PSO存在的早熟收敛问题,全局收敛能力较PSO有较大提高。同时,为提高洪水灾情评估的灾情分辨率,提出一种基于CCPSO及投影寻踪模型的洪灾评估方法,该方法采用一种修正Logistic曲线来建立洪灾评估的投影寻踪模型,并使用CCPSO来优化投影指标函数以及模型参数。仿真应用结果验证了该方法的合理性及有效性。

基于量子混沌映射降低OFDM系统PAPR的算法研究

针对OFDM系统存在较高峰均功率比的问题,提出基于量子loigstic混沌映射的改进选择性映射算法,采用量子loigstic混沌映射作为随机相位序列矢量,解决了传统loigstic混沌映射的不动点和稳定窗问题,提供数目众多,具有良好相关特性和随机特性,易于产生和再生的信号。仿真结果表明所提算法有效降低了系统的峰均比,扩展了候选序列数量,减少了冗余信息传输量,降低了系统的边带功率,并在OFDM技术中具有广阔的应用前景。