A perturbation method to the tent map based on Lyapunov exponent and its application

Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function - the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation.

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

We propose a new fractional two-dimensional triangle function combination discrete chaotic map （2D-TFCDM） with the discrete fractional difference. Moreover, the chaos behaviors of the proposed map are observed and the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits are derived, respectively. Finally, with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem, we apply the discrete fractional map into color image encryption. After that, the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.

Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction,bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multistability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially,this work can be used for some real applications in secure communication, such as data and image encryptions.

A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors

We study a novel class of two-dimensional maps with infinitely many coexisting attractors.Firstly,the mathematical model of these maps is formulated by introducing a sinusoidal function.The existence and the stability of the fixed points in the model are studied indicating that they are infinitely many and all unstable.In particular,a computer searching program is employed to explore the chaotic attractors in these maps,and a simple map is exemplified to show their complex dynamics.Interestingly,this map contains infinitely many coexisting attractors which has been rarely reported in the literature.Further studies on these coexisting attractors are carried out by investigating their time histories,phase trajectories,basins of attraction,Lyapunov exponents spectrum,and Lyapunov(Kaplan–Yorke)dimension.Bifurcation analysis reveals that the map has periodic and chaotic solutions,and more importantly,exhibits extreme multi-stability.

A class of two-dimensional rational maps with self-excited and hidden attractors

This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov(Kaplan–Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work.

1-set-contractive perturbations of accretive operators in Menger PN-spaces

Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menger PN-spaces and obtain some new results.

A note on the perturbed monomial mapping

In this paper, we present a necessary and suffcient condition that the perturbed monomial mapping is ergodic on a sphere S_(p-1)(1), which is in a combination with Anashin's earlier results about the perturbed monomial ergodic mappings on a sphere S_(p-r)(1), r > 1, completely solve a problem posed by A. Khrennikov about the ergodicity of a perturbed monomial mapping on a sphere.

BRUCK FORMULA FOR A PERTURBED LIPSCHITZIAN ITERATION OF LIPSCHITZ PSEUDOCONTRACTIVE MAPS

The solution to evolution equations has developed an independent theory within nonlinear analysis dealing with the existence and approximation of such solution （ fixed point） of pseudocontractive operators and its variants. The object is to introduce a perturbed iteration method for proving the convergence of sequence of Lipschitzian pseudocontractive mapping using approximate fixed point technique. This iteration can be ued for nonlinear operators which are more general than Lipschitzian pseudocontractive operator and Bruck iteration fails for proving their convergence. Our results generalize the results of Chidume and Zegeye.

Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings

In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given.

多策略改进MPA在无线传感器网络中的应用

针对无线传感器网络中非测距节点定位算法自身存在算法定位误差较大的缺陷,提出了一种MMPA-3DDV-Hop算法。该算法先利用多通信半径细化节点间的跳数,然后添加了修正因子修正平均跳距,接着采用多策略融合改进MPA算法计算待定位节点位置最优解。多策略改进MPA算法首先利用Singer混沌映射策略对种群进行初始化,克服种群初始化的盲目性。其次,采用t-分布扰动策略来提升算法的全局搜索能力,在增加搜索空间多样性的前提下,达到快速收敛;最后,引入变异策略和小概率策略,将二者相结合来避免该算法陷入局部最优,对改进算法在复杂度、收敛性和稳定性方面进行性能测试,测试结果表明改进后的MPA算法具有较好的收敛性和稳定性。仿真结果表明:相比3DDV-Hop算法、多通信半径算法以及3D-VNDV-Hop算法,MMPA-3DDV-Hop算法的归一化定位误差平均降低了21.3%、13%与5.7%左右,尽管算法的平均运行时间略有增加,但有效提高了算法的定位精度。

双种群协同演化的改进蜜獾算法

针对蜜獾算法存在的局部搜索能力不足、易陷入局部最优值等问题,提出一种双种群协同演化的改进蜜獾算法。在初始化阶段采用Cubic混沌映射对种群进行初始化,扩大可行解的搜索范围并提高种群的分布均衡性;引入融合黏菌算法和蜜獾算法的双种群优化机制,依托两者的更新优势协同推进个体逼近目标位置,进而提高整个算法的搜索效率和优化性能;采用柯西随机反向扰动策略对蜜獾种群最优位置进行扰动,以提高算法跳出局部最优的能力。通过评估单一策略的改进有效性实验、与七种对比算法的不同高维实验以及Wilcoxon秩和检验,结果表明该算法具有良好的收敛精度和求解速度。最后将改进算法应用于压缩弹簧设计和压力容器设计问题,进一步验证了改进策略的有效性及该算法的工程实用性。

引入精英反向学习和柯西变异的混沌蜉蝣算法

为提高蜉蝣算法的收敛速度,提升算法寻优能力,提出一种引入精英反向学习和柯西变异的混沌蜉蝣算法。利用Circle混沌映射序列优化初始种群使种群分布更加均匀,提高种群多样性。在蜉蝣更新阶段,对蜉蝣中的精英个体进行反向学习策略,防止算法陷入局部最优,提高算法收敛速度。为保证种群进化方向和扩大寻优范围,将自适应概率阈值和柯西变异的扰动机制相结合,对劣势蜉蝣个体附近生成更大的扰动。通过8个基准测试函数实验对比和Wilcoxon秩和检验,实验结果表明,混沌蜉蝣算法在收敛速度、求解精度以及稳定性等方面有较大提高。

多项式变异和自适应权重优化的阿奎拉鹰算法

针对基本阿奎拉鹰算法存在收敛精度低、易陷入局部最优的问题,通过在全局搜索阶段引入多项式变异扰动策略,在局部开发阶段引入自适应权重优化策略,改进了阿奎拉鹰算法的局部探索能力,并且引入了Tent混沌映射初始化种群,增加种群多样性,引入动态转换概率策略来平衡全局探索和局部开发的比重,故提出多项式变异和自适应权重优化的阿奎拉鹰算法。采用基本阿奎拉鹰算法、哈里斯鹰算法、灰狼算法、鲸鱼算法、海鸥算法做对比,9个基准测试函数和2个工程优化问题对改进后的算法进行寻优性能验证,结果表明:改进后的算法在多数测试函数上取得较好的寻优效果,在工程优化问题中,效果优于多数对比算法。证明了改进后的算法具有更快的收敛速度和精度,并在工程应用中取得较好效果。

融合柯西扰动与种群优化的布谷鸟算法

针对传统布谷鸟算法存在的初始种群多样性差、面对高维复杂问题极易陷入局部最优解的问题,采用Tent混沌映射优化初始种群,使初始种群具有更好的便利性,对多次迭代中当代最优值不变的种群进行柯西扰动,提高算法跳出局部最优解的能力。采用7种不同类型的测试函数与CS、PSO、DE3种对比算法,验证改进算法的寻优能力。结果表明,对于不同类型的测试函数,改进的算法较传统算法在寻优速度与精度方面均有所提高。

基于VMD-ISSA-LSTM的短时交通流预测研究

针对城市短时交通流随机波动性强、可靠性低、预测精度差等问题,将变分模态分解(VariationalMode Decomposition,VMD)和改进麻雀搜索算法(ImproveSparrowSearchAlgorithm,ISSA)与长短期记忆(LongShort-Term Memory, LSTM)神经网络相结合,建立一种短时交通流预测模型(VMD-ISSA-LSTM)。首先利用VMD对历史原始交通流数据进行分解;然后采用佳点集、正弦函数扰动和Tent混沌映射等策略对标准的SSA算法加以改进,增强ISSA算法的寻优能力;最后,将每个分量送入ISSA-LSTM中进行预测,同时将预测结果线性叠加,得到交通流量预测值。以上海市中山北路-曹杨路口2018年11月1日—30日的历史交通数据对模型进行验证。结果表明,与LSTM、VMD-LSTM、VMD-SSA-LSTM等传统预测模型相比,VMD-ISSA-LSTM模型的预测结果的平均绝对百分比误差为1.278 4%,能够更好地应用于短时交通流预测中。

强化哈里斯鹰算法求解柔性车间调度问题

针对以最小化最大完工时间为优化目标的单目标柔性作业车间调度问题,本文提出了强化哈里斯鹰优化算法。通过Circle混沌映射改进算法初始种群的质量,提高算法的收敛速度;采用正余弦策略改进逃逸能量的变化方式,并将逃逸能量与跳跃强度相结合,以此提升算法的全局探索能力,预防算法陷入局部最优;使用柯西扰动的差分进化策略提高算法的局部搜索能力以及寻优性能。通过柔性作业车间调度问题典型算例的对比试验,验证了强化哈里斯鹰算法能够有效求解柔性作业车间调度问题。

考虑恶化效应的MapReduce模型下的同类机调度

本文研究了MapReduce模型中考虑恶化效应的同类机调度问题.在MapReduce模型中每个工件加工必须经过两道工序.其中在第1道工序中每个工件加工任务可分割成若干个子任务且能并行加工,当某个工件中的所有子任务全部完成后,才允许启动第2道工序,且第2道工序只能在一台机器上连续加工.本文考虑了工件实际加工时间与其开工前的等待时间呈线性函数关系的恶化效应,构建了以最小化所有工件的逗留时间和为目标函数的混合整数规划模型,同时给出了问题的一个下界,最后设计了采用正余弦差分扰动机制的改进蝙蝠优化算法来求解模型.通过数值仿真对蝙蝠优化算法、遗传算法、CPLEX结果与下界进行对比,验证了模型的正确性和改进算法的有效性.

求解逆运动学的多策略蜻蜓算法

蜻蜓算法(Dragonfly Algorithm,DA)是一种新型群智能算法,存在求解精度不高、收敛速度慢、优化不稳定等不足.基于此,提出了一种多策略改进的蜻蜓算法(Multi-strategy Improved Dragonfly Algorithm,MIDA).首先通过Logistic混沌映射改善算法的初始种群,使算法能更快锁定最优解区域;其次融合共生生物搜索算法(Symbiotic Organisms Search,SOS)来增加个体间的信息交流;最后采用了余弦扰动避免蜻蜓算法过早陷入局部最优解,并且采用正交实验验证该算法的可行性.通过12个基准函数和求解逆运动学这一实际应用来验证MIDA的有效性.结果表明,MIDA在函数优化方面遥遥领先,在求解逆运动学问题中,优化效果比其他对比算法高10%~35%.

有限精度下Skew Tent映射的抗退化研究

混沌是指确定性动力学系统在初值变化细微的情况下,经过足够多的迭代后表现出来的不可预测性、类随机性的非周期性运动。随着混沌系统在通信工程、密码学、图像加密等方向的应用,有限精度下混沌系统动力学性能退化的问题就随之出现。提高混沌系统有限精度下的动力学性能有多种方法,其中,直接提升应用环境计算精度的代价太大、实际操作性不强。文中从提高混沌系统的抗退化性能方向入手,提出一种利用Lorenz系统对Skew Tent进行参数、输出扰动,从而提高Skew Tent系统的抗退化性能的方法,同时也克服了Skew Tent系统会进入不动点的情况。随后通过对改进后的系统进行初值敏感性、回归映射、自相关性、近似熵测试以及对量化后混沌序列进行NIST测试,结果表明使用该方案改进后的Skew Tent系统具有良好的混沌性,在通信工程、混沌密码算法设计、图像加密等方面有良好的应用前景。

Approximate Perturbation Stance Map of the SLIP Runner and Application to Locomotion Control

This paper presents a novel method of perturbation to obtain the analytic approximate solution to the Spring-Loaded Inverted Pendulum （SLIP） dynamics in stance phase with considering the effect of gravity. This perturbation solution achieves higher accuracy in predicting the apex state variables than the typical existing analytic approximations. Particularly, our solution is validated for non-symmetric trajectory of hopping in a large angle range. Furthermore, the stance controller of the SLIP runner is developed to regulate the apex state based on the approximate apex return map. To compensate the energy variation between the current and desired apex states, a stiffness adjustment of the leg spring in stance phase is presented. The deadbeat controller of the angle of attack is designed to track the regulated apex height and velocity. The simulation demonstrates that the SLIP runner applying the proposed stance controller reveals higher tracking accuracy and more rapidly converges to the regulated apex state.