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.

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.

Syntactic Characteristics and a Smart Construction Mechanism for Thematic Map Symbols

The construction of thematic map symbols is a very complex and intellectually demanding process,but thematic symbols can be automatically generated and easily shared on the web using the syntactic structure of semantic symbols.In this paper,the symbol types,inner structure,and design pattern are discussed.A syntactic construction theory based on letter (thematic maps primitive)-word (single thematic symbol)-sentence (combined symbols or complex symbols) structure model is proposed to automate the construction of thematic map symbols.As a result of this research,symbols can be defined using cartographic primitives which are arranged according to syntactic principles.A semiotic model and word-centered construction theory can be integrated into interactive cartography as represented by the technology of Internet.Finally,the concepts and schema of this theory are discussed,and some examples are presented based a web thematic cartographic system to verify its utility.

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 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.

Construction of Forestry Map Symbol Library and Symbolization Execution Based on MapGIS K9

In order to improve the cartography efficiency and the intelligent level of forestry map,we put forward the symbolization scheme of forestry map based on MapGIS K9 platform.Firstly,the symbol library of forestry map was constructed according to The Graphic Representation of Forestry Map which was issued by the National Forestry Bureau in October,2010.Then,the symbol configuration rule database was established to realize the expression of symbol configuration rule in the digital environment.Finally,the symbolization module was realized with the support of MapGIS Objects component development technology,and the thematic data of forestry were visualized according to the symbol configuration rule.The practice proved that the scheme could basically satisfy the cartography requirements of common forestry maps which included the forest management inventory map.

On new chaotic mappings in symbol space

A well known chaotic mapping in symbol space is a shift mapping.However,other chaotic mappings in symbol space exist too.The basic change is to consider the process not only at a set of times which are equally spaced,say at unit time apart（a shift mapping）,but at a set of times which are not equally spaced,say if the unit time can not be fixed.The increasing mapping as a generalization of the shift mapping and the k-switch mapping are introduced.The increasing and k-switch mappings are chaotic.

Algorithm of symbol generation and configuration of land polygons in present land-use map

The symbolization of land polygon is an important part of cartography. In the mapping of traditional present land-use maps, the symbol of land polygons was usually filled by the method of filling or plotting, but these methods can't solve the spatial conflicts of the symbol. According to the principle of cartography, the rule of how to symbolize the land polygon was summarized, and a new method that can generate and deploy the land symbols was presented. By making use of C# programming language and Arc Engine developing components, the algorithm can generate land symbols presenting triangle and adjust the coordinate of the symbol. Through mapping the present land-use map of Honghe county, this algorithm can reduce 88.84% of the spatial conflicts error rate compared with the traditional methods. It improves the accuracy and efficiency of the map symbolic.

Studies of phase return map and symbolic dynamics in a periodically driven Hodgkin–Huxley neuron

How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional （1D） map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm -- symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.

A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics

Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices （CMLs）. It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence （CD）. Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to- noise ratios （SNRs） are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors usiug symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.

A method of estimating initial conditions of coupled map lattices based on time-varying symbolic dynamics

A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices （CMLs）. The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer-Rao lower bound （CRLB） than that with the time-invariant estimation method, especially at high signal-to-noise ratios （SNRs）.

Symbolic dynamics of Belykh-type maps

The symbolic dynamics of a Belykh-type map （a two-dimensional discon- tinuous piecewise linear map） is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.

An Anti-aliasing Algorithm Suitable to Map Publishing Symbol

On the basis of analysis of various algorithms, an anti-aliasing algorithm called brush method was presented, which is suitable to map publishing symbol. After introducing the basic principle and implementation of brush method in detail, the result and efficiency were evaluated through experiments.

Enhanced cooperative packet retransmission employing joint cooperative diversity and symbol mapping diversity

A joint cooperation diversity and symbol mapping diversity (SMD) strategy is proposed for cooperative packet retransmission system with high-order modulation such as 16QAM. Substantial SER/BER (symbol error rate/bit error rate) gains result from multiple packet transmissions over independent paths and distinct bit-to-symbol mappings for each packet transmis-sion. The SER/BER performance of relay assisted retransmission system is analyzed. Simulation results show that the joint-diversity strategy can provide more BER gains than other relaying strategies (i.e., decode-and-forward and constellation rearrangement relaying strategies) when no relay makes a decision error; but if some relays make decision errors, the joint-di-versity strategy outperforms other relaying strategies only when the relays are closer to the source than to the destination.

Bandwidth Efficient Three-User Cooperative Diversity Scheme Based on Relaying Superposition Symbols

Recently, Cooperative diversity in wireless communication systems has gained much attention. A simple two-user cooperative diversity scheme called decode-and-forward cooperation scheme has been presented by Laneman (2004). Each user has one partner to decode its information and retransmit it by employing repeti-tion coding. This scheme can offer diversity order of two. But the bandwidth efficiency is low. In this paper, we propose a bandwidth efficient three-user cooperative diversity scheme based on relaying superposition symbols. Each user has two partners and each partner relays superposition symbols of the other two users instead of repetition. Thus, the bandwidth efficiency is improved compared to the baseline decode- and-forward cooperative diversity scheme presented by Laneman. Moreover, the proposed scheme can also offer diversity order of two. Then, in order to improve the system performance, a new constellation labeling for the superposition 8PSK modulation is designed. It is a simple way to exploit the symbol mapping diver-sity and a gain of about 2 dB can be obtained. Furthermore, the performance improvement comes at no addi-tional power or bandwidth expense.

基于MAPGIS的全国地质工作程度数据库应用系统设计与实现

二十世纪在全国开展了大量地质调查工作,并且建立起“全国地质工作程度空间数据库”,急需研发应用系统保障该数据库作用的充分发挥。这里运用GIS软件工程原理,对应用系统进行了需求分析和系统分析,特别是对各重要模块进行了详细设计。该应用系统已基于MAPGIS 6.x实现,几项特色功能被重点展示,它们为保障整个系统功能起到了关键性的作用。

基于Autodesk Map地图符号库的设计与开发

在地图数字化过程中,经常需要使用一些专门的点、线、面符号来表示特定的地物,而在AutodeskMap的标准符号库中没有这类地图符号.为避免重复繁琐地绘制这些符号实体,在AutodeskMap环境下,依据地图符号的一般特点和编码原则,根据点、线和面符号复杂程度和结构形状的不同,采用定制法、PDB开发方法和ObjectARX二次开发方法,设计并创建了特定地物的地图符号库.

基于MapObjects的特殊点符号制作和旋转

结合研究项目"河南省内河航道基础地理信息系统",利用Visual Basic和MapObjects开发了航道系统专门的符号库,使用FontCreator字体软件制作所需符号,然后根据点符号旋转算法,利用渲染方法实现了有向点符号不同角度的旋转。

MapInfo下地图符号库的制作

分析了MapInfo符号制作技术原理,结合地形图点、线、面符号的特点,给出了一组符号制作的具体实例。

基于MapInfo的土地利用现状图符号库的设计与实现

MapInfo系统自带的符号库不能满足我国各种比例尺土地利用现状图的需要,通过分析MapInfo符号的建库原理和方法,同时结合土地利用现状图符号的特点,采用实验的方法解决符号制作的尺寸规律问题,设计、开发了满足国标要求的土地利用现状图符号库,并用实例对符号库的应用做了分析与探讨。