A novel variable-order fractional chaotic map and its dynamics

In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.

On new classes of strongly Janowski type functions of complex order

We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,analytic properties of these classes under certain integral operator are also discussed.Our findings are more comprehensive than the existing results in the literature.

Outer synchronization between two different fractional-order general complex dynamical networks

Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper.Based on the stability theory of the fractional-order system,the sufficient criteria for outer synchronization are derived analytically by applying the nonlinear control and the bidirectional coupling methods.The proposed synchronization method is applicable to almost all kinds of coupled fractional-order general complex dynamical networks.Neither a symmetric nor irreducible coupling configuration matrix is required.In addition,no constraint is imposed on the inner-coupling matrix.Numerical examples are also provided to demonstrate the validity of the presented synchronization scheme.Numeric evidence shows that both the feedback strength k and the fractional order α can be chosen appropriately to adjust the synchronization effect effectively.

Decentralized Adaptive Strategies for Synchronization of Fractional-order Complex Networks

This paper focuses on synchronization of fractionalorder complex dynamical networks with decentralized adaptive coupling.Based on local information among neighboring nodes,two fractional-order decentralized adaptive strategies are designed to tune all or only a small fraction of the coupling gains respectively.By constructing quadratic Lyapunov functions and utilizing fractional inequality techniques,Mittag-Leffler function,and Laplace transform,two sufficient conditions are derived for reaching network synchronization by using the proposed adaptive laws.Finally,two numerical examples are given to verify the theoretical results.

Approximate Solutions to the Discontinuous Riemann-Hilbert Problem of Elliptic Systems of First Order Complex Equations

Several approximate methods have been used to find approximate solutions of elliptic systems of first order equations. One common method is the Newton imbedding approach, i.e. the parameter extension method. In this article, we discuss approximate solutions to discontinuous Riemann-Hilbert boundary value problems, which have various applications in mechanics and physics. We first formulate the discontinuous Riemann-Hilbert problem for elliptic systems of first order complex equations in multiply connected domains and its modified well-posedness, then use the parameter extensional method to find approximate solutions to the modified boundary value problem for elliptic complex systems of first order equations, and then provide the error estimate of approximate solutions for the discontinuous boundary value problem.

Generalized projective synchronization of fractional-order complex networks with nonidentical nodes

This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 < q < 1 is obtained based on the stability theory of the fractional-order system.The control method which combines active control with pinning control is then suggested to obtain the controllers.Furthermore,the adaptive strategy is applied to tune the control gains and coupling strength.Corresponding numerical simulations are performed to verify and illustrate the theoretical results.

UV-Vis Spectrum and the Third-order Nonlinear Optical Properties of the Chiral Camphorderived β-diketonate Platinum Complexes

UV-Vis spectrum and the third-order nonlinear optical properties of the chiral camphor-derived β-diketonate have been studied at the B3LYP/6-31G* level. The results showed that the introduction of electron-drawing group-CF3 and-C3F7 on β-diketonate made the strongest absorption peak red-shift and the lowest energy absorption blue-shied. Introduction of-OC2H5 on the benzene or pyridine ring made the lowest energy absorption blue-shift. When the-C2H3 was introduced on the benzene or pyridine ring, the lowest energy absorption was red-shifted. Introduction of electron-donating group on β-diketonate can enlarge their nonlinear optical properties. On the contrary, the introduction of electron-drawing group dropped it down.

Selecting suitable key supplier for core components during smart complex equipment central-private enterprises collaborative development process:from two different forms of evaluation information and matching perspective

With the development of central-private enterprises integration,selecting suitable key suppliers are able to provide core components for smart complex equipment.We consider selecting suitable key suppliers from matching perspective,for it not only satisfies natural development of smart complex equipment,it is also a good implementation of equipment project in central-private enterprises integration context.In in this paper,we carry out two parts of research,one is evaluation attributes based on comprehensive analysis,and the other is matching process between key suppliers and core components based on the matching attribute.In practical analysis process,we employ comprehensive evaluated analysis methods to acquire relevant attributes for the matching process that follows.In the analysis process,we adopt entropy-maximum deviation method(MDM)-decision-making trial and evaluation laboratory(DEMATEL)-technique for order preference by similarity to an ideal solution(TOPSIS)to obtain a comprehensive analysis.The entropy-MDM is applied to get weight value,DEMATEL is utilized to obtain internal relations,and TOPSIS is adopted to get ideal evaluated solution.We consider aggregating two types of evaluation information according to similarities of smart complex equipment based on the combination between geometric mean and arithmetic mean.Moreover,based on the aforementioned attributes and generalized power Heronian mean operator,we aggregate preference information to acquire relevant satisfaction degree,then combine the constructed matching model to get suitable key supplier.Through comprehensive analysis of selecting suitable suppliers,we know that two-sided matching and information aggregation can provide more research perspectives for smart complex equipment.Through analysis for relevant factors,we find that leading role and service level are also significant for the smart complex equipment development process.

Crystal Structure and Third-order Nonlinear Optical Property Studies on Copper(Ⅱ) Complex Containing NS Donor Ligand

A novel Schiff base ligand (HL) derived from S-methyldithiocabazate and pmethoxylbenzaldehyde was prepared and characterized. The Schiff base ligand acts as a single negatively charged bidentate ligand fondng D-M-D type comPlex (D=donor, M=metal). Single crystal X-ray diffraction analysis of the copper(Ⅱ) complex established that the geometry around Cu (Ⅱ) is square-planar with two equivalent M-N and M-S bonds. The two phenyl rings and the coordinated plane are almost in one plane fotheng an electronic delocalization system. Their thirdorder response was also studied.

Attempt to generalize fractional-order electric elements to complex-order ones

The complex derivative D^(α±jβ), with α, β∈ R+ is a generalization of the concept of integer derivative, where α = 1,β = 0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complexorder electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed.Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system.

Fractional-Order Modeling and Dynamical Analysis of a Francis Hydro-Turbine Governing System with Complex Penstocks

This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-turbine governing system with complex penstocks is built from an engineering application perspective. This model is described by state-space equations and is composed of the Francis hydro-turbine model, the fractional-order complex penstocks model, the third-order generator model, and the hydraulic speed governing system model. Based on stability theory for a fractional-order nonlinear system, this study discovers a basic law of the bifurcation points of the above system with a change in the fractional-order a. Secondly, the stable region of the governing system is investigated in detail,and nonlinear dynamical behaviors of the system are identified and studied exhaustively via bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Results of these numerical experiments provide a theoretical reference for further studies of the stability of hydropower stations.

Riemann-Hilbert problem for first order complex equations of mixed type with degenerate curve

This paper considers the Riemann-Hilbert problem for linear mixed(elliptichyperbolic) complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.

Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application

Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link.In this paper,considering the complex network with uncertain parameters,new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization(FTCPS).In addition,based on fractional-order Lyapunov functional method and finite-time stability theory,the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters.Meanwhile,numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters.Finally,the network is applied to image encryption,and the security analysis is carried out to verify the correctness of this method.

Hybrid Synchronization of Fractional-Order Complex Networks Model via Fractional Order Controller

For the purpose of investigating two complex networks' hybrid synchronization,a controller with fractional-order is provided.Regarding hybrid synchronization which includes the outer synchronization and inner synchronization,some hybrid synchronization's sufficient conditions according to the Lyapunov stability theorem and the LaSalle invariance principle are proposed.Theoretical analysis suggests that,only when the state of driving-response networks is outer synchronization and each network is in inner synchronization,two coupled networks' hybrid synchronization under some suitable conditions could be reached.Finally,theoretical results are illustrated and validated with the given numerical simulations.

Synthesis, Structure and Third-order Non-linear Optical Properties of Tungsten Dioxo Complex with 8-Hydroxyquinoline Ligand WO_2(C_9H_6NO)_2

Tungsten dioxo complex WO 2(C 9H 6NO) 2 was obtained via the low temperature solid-state reaction of(NH 4) 2WS 4, 8-hydroxyquinoline(8-hq) and(CH 3) 4NI, and it was characterized by means of elemental analyses, IR spectroscopy and X-ray diffraction analysis. The crystal of the title compound belongs to monoclinic, space group C2/c, with the crystal cell parameters: a=1.3316(3) nm, b=0.94444(19) nm, c=1.3485(3) nm, β=109.66(3)°, V=1.5970(6) nm 3, Z=6. The title compound possesses a supramolecular structure formed through hydrogen bonds and π-π stacking interactions. The third-order non-linear optical(NLO) properties of the title compound were also investigated. The third-order non-linear absorption coefficient α 2 and refractive index n 2 are 0.85×10 -11 m/W -1 and -1.5×10 -19 m 2/W, respectively. The third-order non-linear susceptibility χ (3) is 3.03×10 -13 esu for 3.8×10 -5 mol/L sample concentration.

Investigation on Third-Order Optical Nonlinearities of Two Organometallic Dmit2- Complexes Using Z-Scan Technique

The third-order nonlinear optical properties of two dmit organometallic complexes, [(CH3)4N] [Au(C3S5)2] (MeAu) and [(CH3)4N][Ni(C3S5)2] (Me Ni) in acetone solutions, were characterized us- ing a short pulse Z-scan technique at 1064 nm wavelength. Self-defocusing effects were found in both samples and stronger saturable absorp-tion was observed in MeNi solution comparing with that of MeAu. The origins were analyzed for the differences between the results. Two figures of merit W and T were also calculated to evalu-ate the suitability of two materials for all-optical integrated devices. The results of W=22.84 and T≈0 of MeAu make it an excellent candidate for the all-optical applications.

基于RKADE-SS-FDTD方法的无条件稳定高阶CFS-PML算法

为了提升完全匹配层(PML)算法的吸收效果,提出了一种用于截断非磁化等离子体的高阶复频率偏移PML(HO-CFS-PML)算法。该算法将龙格-库塔辅助微分方程(RKADE)算法和分裂步时域有限差分(SS-FDTD)算法相结合,来对非磁化等离子体进行仿真。在计算域边界处,引入了由辅助微分方程(ADE)算法实现的HO-CFS-PML用于截断开放区域中的等离子体,并通过一个数值算例进行模拟。结果表明:所提出的HO-RKADE-SS-CFS-PML算法在柯朗-弗里德里希斯-列维(CFL)数(CFLN)为8时,相比于传统CFS-PML算法,时间减少率可以达到79.2%,证明了该算法能够有效地消除柯朗-弗里德里希斯-列维(CFL)稳定性条件的约束,大大节省了计算时间;此外,HO-RKADE-SS-CFS-PML算法的最大相对反射误差可以达到-115 dB,明显小于其他算法的相对反射误差,并且随着CFLN的增大,该算法不会像RKADE-ADI-CFS-PML算法那样产生明显的误差增大现象,证明本文算法在大时间步长下拥有比其他算法更好的吸收电磁波的能力。

基于通用可调(p,q)阶Rife-Vincent自乘-卷积窗的改进四谱线插值高精度谐波分析算法

加窗快速傅里叶变换(WIFFT)是一类重要的谐波参数估计方法。然而,快速傅里叶变换固有的栅栏效应以及非同步采样产生的频谱泄漏对谐波参数的估计精度有较大影响。为此,利用具有最大旁瓣衰减特性的I类Rife-Vincent窗作为父窗,提出一种新型的通用可调(p,q)阶Rife-Vincent自乘-卷积窗(RVSMC p-q),其特点在于通过改变乘积阶数和卷积阶数可以灵活地改变窗函数的主瓣宽度、旁瓣峰值和衰减速度。在此基础上,提出一种基于RVSMC p-q窗的四谱线插值高精度谐波参数估计方法,利用最小二乘拟合原理给出谐波信号的幅值、频率及相位参数的低复杂度多项式估计公式。在复杂谐波、间谐波及基波频率波动的情况下对基于RVSMC p-q窗的四谱线插值谐波参数估计方法的效果进行仿真。研究结果表明:在较低的乘积和卷积阶数条件下,新算法可以获得比经典的基于自乘积窗或自卷积窗的WIFFT算法更为优越的参数估计精度,且算法复杂度较低。

Fluid-based Slotting Optimization for Automated Order Picking System with Multiple Dispenser Types

Slotting strategy heavily influences the throughput and operational cost of automated order picking system with multiple dispenser types, which is called the complex automated order picking system (CAOPS). Existing research either focuses on one aspect of the slotting optimization problem or only considers one part of CAOPS, such as the Low-volume Dispensers, to develop corresponding slotting strategies. In order to provide a comprehensive and systemic approach, a fluid-based slotting strategy is proposed in this paper. The configuration of CAOPS is presented with specific reference to its fast-picking and restocking subsystems. Based on extended fluid model, a nonlinear mathematical programming model is developed to determine the optimal volume allotted to each stock keeping unit (SKU) in a certain mode by minimize the restocking cost of that mode. Conclusion from the allocation model is specified for the storage modules of high-volume dispensers and low-volume dispensers. Optimal allocation of storage resources in the fast-picking area of CAOPS is then discussed with the aim of identifying the optimal space of each picking mode. The SKU assignment problem referring to the total restocking cost of CAOPS is analyzed and a greedy heuristic with low time complexity is developed according to the characteristics of CAOPS. Real life application from the tobacco industry is presented in order to exemplify the proposed slotting strategy and assess the effectiveness of the developed methodology. Entry-item-quantity (EIQ) based experiential solutions and proposed-model-based near-optimal solutions are compared. The comparison results show that the proposed strategy generates a savings of over 18% referring to the total restocking cost over one-year period. The strategy proposed in this paper, which can handle the multiple dispenser types, provides a practical quantitative slotting method for CAOPS and can help picking-system-designers make slotting decisions efficiently and effectively.