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.

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.

A Prelude Staircase to a Type V Intermittency in Two—Dimensional Discontinuous Maps

A sequence of periodic attractors has been observed in a two-dimensional discontinuous map, which canbe considered as a model of impact oscillator. The so-called 'transfer number', which is defined as the mean numberof transfer from non-impact state to impact state per iteration, is locked onto a lot of rational values to form a curveconsisting of many steps. Our numerical investigation confirms that every step is confined by conditions created by thecollision between the periodic orbit and the discontinuous boundary of the system. After the last collision the systemshows a chaotic motion with intermittent characteristics. Therefore the staircase can be addressed as a 'prelude staircaseto type V intermittency'. The similar phenomenon has also been observed in a model of electric circuit. These resultsof our study suggest that this kind of staircases is common in two (or even higher) dimensional discontinuous maps.

Two-dimensional gel electrophoresis analysis of the proteomes expressed in the human hepatoma cell line BEL-7404 and normal liver cell line L-02

Proteome analysis technology has been used extensively in conducting discovery research of biology and has become one of the most essential technologies in functional genomics. The proteomes of the human hepatoma cell line BEL-7404 and the normal human liver cell line L-02 have been separated by high resolution two-dimensional gel electrophoresis (2-DE) with immobilized pH gradient isoelectric focusing (IPG-IEF) in the first dimension and sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) in the second dimension (IPG-DALT). The resulting images have been analyzed using 2-D analysis software. Quantitative analysis reveals that 7 protein spots are detected only in hepatoma BEL-7404 cells, 14 only in L-02 cells, and 78 protein spots show significant fluctuation in quantity in both cell lines (P【0.01). These protein spots have been displayed on a proteome differential expression map. Analysis for the reproducibility of 2-DE indicates that the positional variability in the IEF dimension

Proteome Analysis of Neisseria meningitidis Serogroup Strains C Associated with Outbreaks in China

Objective During 2003-2005, an outbreak of meningitis due to Neisseria meningitidis serogroup C occurred in China. With the aim to find strain clues result in the final epidemics, the ancestral strain 053442, a clinical isolate, and a carrier strain 053426 with different gene type were analyzed. Methods Clinical strain 053442 and carrier strain 053426 were cultured on GC agar plates under the same condition. Two-dimensional electrophoresis was performed using the pH 3–10 nonlinear IPG strips of 24 cm length, and all the protein spots were identified by matrix-assisted laser desorption/ionization time of flight spectrometry. Results 502 and 380 protein spots were identified in 053426 and 053442 respectively, relating to 266 and 202 different genes covering a wide range of cellular functions. The express volume and number of proteins involved in energy metabolism, protein synthesis and amino acid biosynthesis in 053426 were higher than in 053442. Virulence factor Opa, Opc and a series of proteins involved in pilus assembly and retraction were identified in 053442, which appear to be of primary importance in colonization and invasion of human cells. Compared to 053442, virulence protein species were less in 053426, with lower express volumes too. No Opa and Opc were detected in 053426. Conclusion The different protein expression profiles of the clinical strain 053442 and carrier strain 053426 in the present study provide some clues of the different pathogenicity of the two strains, which may account for result in the final epidemics.

Comparative Proteomic Analysis of <i>Helicobacter pylori</i>Strains Isolated from Chinese Patients

Helicobacter pylori, the major cause of gastritis, peptic ulcer and gastric cancer, infects half of the world population, but only a few infections lead to serious disease. In order to investigate specific proteins related to the pathogenic difference of this bacterium, comparative proteome analyses of Helicobacter pylori C1 (isolated from patients with gastric cancer) and G1 (isolated from patients with gastritis) were performed using two-dimensional gel electrophoresis (2-DE) and matrix-assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF MS). Four proteins (inorganic pyrophosphatase, 3-oxoadipate CoA-transferase subunit B, translation elongation factor, and aldo-keto reductase) were found only in Helicobacter pylori C1, and one protein (alkyl hydroperoxide reductase) was found in G1. Additionally, different isoelectric points (pI) of Hsp60 were observed from the two strains. Then we cloned and sequenced Hsp60 genes from forty-nine Helicobacter pylori isolated from gastric cancer and gastritis. Gene sequencing showed that one C→G single nucleotide polymorphism occurred in the 1399th nucleotide of Hsp60. These results indicate that pathogenic differences exist in various Helicobacter pylori isolated from Chinese patients.

High-precision analytical solutions for Earth coverage of constellation equipped with reentry glide vehicles

To efficiently and accurately design satellite constellations equipped with Reentry Glide Vehicles(RGVs),new analytical solutions are developed for calculating their coverage perfor-mance.Specifically,a new coverage model is established by approximating the Reentry Reachable Domain(RRD).However,the computation of real-time relative distances between satellites and targets,which is essential for coverage analysis based on this model,imposes a significant compu-tational burden.To address this challenge,a coverage analysis method based on two-dimensional map theory is proposed.This method represents the coverage conditions of a target as a fixed area on a two-dimensional map and transforms the satellite trajectory into a series of parallel lines.By determining the intersection points between these lines and the area boundaries,the coverage ana-lytical solutions for a target point are derived.On this basis,coverage theorems are presented for rapid calculation of the constellation coverage performance for an area.Simulation results demon-strate the effectiveness and high precision of the proposed analytical solutions.

Towards the Jacobian Conjecture

We first show that if there is a counterexample to the two-dimensional Jacobian conjecture,then there exists a nonempty closed smooth affine surface in C^(2)×C^(2)satisfying various properties.Next,we conjecture that such a surface does not exist.

Establishment of an HPLC method for the analysis of biapenem and its impurities

An HPLC method for routine quality control of biapenem was established.A Dikma Diamonsil C_(18) column(250mm×4.6 mm,5μm) was used with diode array detection and single wavelength detection at 220 nm.The mobile phase was consisted of acetonitrile-0.1%triethylamine water(1:99,v/v).The liner range for biapenem quantification was 0.05-10.0 mg/mL(r^2= 0.999). The LOD and LOQ of impurity were 4.8 ng(S/N = 3) and 18.5 ng(S/N = 10),respectively.Intra-day RSD of main impurity and total impurity were 1.84%and 3.37%(n = 3);inter-day RSD of main impurity and total impurity were 4.84%and 7.58% (n = 9).The test solution was stable when stored at 4℃for 6 h.The impurity peaks of biapenem can be identified by chromatographic spectral correlation analysis using high-performance liquid chromatography-diode array detection data from the quality control method by calculating correlation coefficients without reference standards.Two hydrolysis degradation products with relative retention times(RRTs) of 0.528 and 0.743,two dimers with RRTs of 1.062 and 2.817 were identified in the quality control chromatogram.It provides a new way to identify impurity peaks by the routine HPLC-UV method.

Establishment of an HPLC method for the analysis of biapenem and its impurities

An HPLC method for routine quality control of biapenem was established. A Dikma Diamonsil Cls column （250 mm× 4.6 mm, 5 μm） was used with diode array detection and single wavelength detection at 220 mm. The mobile phase was consisted of acetonitrile-0 1% triethylamine water （1：99, v/v）. The liner range for biapenem quantification was 0.05-10.0 mg/mL （r2- 0.999）. The LOD and LOQ of impurity were 4.8 ng （S/N 3） and 18.5 ng （S/N = 10）, respectively. Intra-day RSD of main impurity and total impurity were 1.84% and 3.37% （n = 3）; inter-day RSD of main impurity and total impurity were 4.84% and 7.58% （n = 9）. The test solution was stable when stored at 4 ℃ for 6 h. The impurity peaks of biapenem can be identified by chromatographic spectral correlation analysis using high-performance liquid chromatography~tiode array detection data from the quality control method by calculating correlation coefficients without reference standards. Two hydrolysis degradation products with relative retention times （RRTs） of 0.528 and 0.743, two dimers with RRTs of 1.062 and 2.817 were identified in the quality control chromatogram. It provides a new way to identify impurity peaks by the routine HPLC-UV method.

Analytical solutions for Earth discontinuous coverage of satellite constellation with repeating ground tracks

This paper presents an analytical model for calculating the Earth discontinuous coverage of satellite constellation with repeating ground tracks by integrating and extending the application of coverage region and route theory.Specifically,the visibility condition for a ground point is represented as a coverage region in the two-dimension map of visibility properties,and the trajectories of satellites with circular orbits and repeating ground tracks are converted to several inclined lines in the map.By analyzing the intersections of the lines and the edge of the coverage region,the coverage durations for the ground point can be calculated.Based on the point coverage,the variations of coverage characteristics along the parallel are analyzed,and the regional or global coverage characteristics of constellations can be obtained.Numerical examples show that the proposed method can accurately and rapidly calculate the coverage characteristics,e.g.revisit time and coverage time.The calculated results are extremely close to those of the Satellite Tool Kit(STK)and are also superior to the existing research results.The proposed analytical model can be a useful tool for constellation design and coverage performance analysis.

Spatial chaos-based image encryption design

In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, permutation and sub- stitution methods are incorporated to present a stronger image encryption algorithm. Spatial chaotic maps are used to realize the position permutation, and to confuse the relationship between the ci- pher-image and the plain-image. The experimental results demonstrate that the suggested encryption scheme of image has the advantages of large key space and high security; moreover, the distribution of grey values of the encrypted image has a random-like behavior.

GLOBAL ANALYSIS OF AN EBENMAN＇S MODEL OF POPULATION WITH TWO COMPETING AGE CLASSES

Several global conclusions about an Ebenman's model of a population with competing juveniles and adults are derived in this paper. The problems about the number of non-trivial fixed points, the number of synchronous 2-cycles, and the number of attracting synchronous cycles are resolved. In a special case, the twice iteration of the 2-dimensional map can be reduced to a 1-dimensional map, and the existence of one or more continua of non-synchronous 2-cycles is pointed out. Numerical calculations are used to draw orbit diagrams which show complicated dynamics of this non-invertible 2-dimensional map. Experimental and field observational evidence is also discussed.

Nanoscience and the nano-bioelectronics frontier

This review describes work presented in the 2014 inaugural Tsinghua University Press-Springer Nano Research Award lecture, as well as current and future opportunities for nanoscience research at the interface with brain science. First, we briefly summarize some of the considerations and the research journey that has led to our focus on bottom-up nanoscale science and technology. Second, we recapitulate the motivation for and our seminal contributions to nanowire- based nanoscience and technology, including the rational design and synthesis of increasingly complex nanowire structures, and the corresponding broad range of ＂applications＂ enabled by the capability to control structure, com- position and size from the atomic level upwards. Third, we describe in more detail nanowire-based electronic devices as revolutionary tools for brain science, including （i） motivation for nanoelectronics in brain science, （ii） demonstration of nanowire nanoelectronic arrays for high-spatial/high-temporal resolution extracellular recording, （iii） the development of fundamentally-new intracellular nanoelectronic devices that approach the sizes of single ion channels, （iv） the introduction and demonstration of a new paradigm for innervating cell networks with addressable nanoelectronic arrays in three-dimensions. Last, we conclude with a brief discussion of the exciting and potentially transformative advances expected to come from work at the nanoelectronics-brain interface.