International Journal of Bifurcation and Chaos

This paper studies complex systems using a generalized multidimensional scaling (MDS) technique. Complex systems are characterized by time-series responses, interpreted as a manifestation of their dynamics. Two types of time-series are analyzed, namely 18 stock markets and the gross domestic product per capita of 18 countries. For constructing the MDS charts, indices based on parametric entropies are adopted. Multiparameter entropies allow the variation of the parameters leading to alternative sets of charts. The final MDS maps are then assembled by means of Procrustes’ method that maximizes the fit between the individual charts. Therefore, the proposed method can be interpreted as a generalization to higher dimensions of the standard technique that represents (and discretizes) items by means of single “points” (i.e. zero-dimensional “objects”). The MDS plots, involving one-, two- and three-dimensional “objects”, reveal a good performance in capturing the correlations between data.

With the aid of sophisticated photo-editing software, such as Photoshop, copy-move image forgery operation has been widely applied and has become a major concern in the field of information security in the modern society. A lot of work on detecting this kind of forgery has gained great achievements, but the detection results of geometrical transformations of copy-move regions are not so satisfactory. In this paper, a new method based on the Polar Complex Exponential Transform is proposed. This method addresses issues in image geometric moment, focusing on constructing rotation invariant moment and extracting features of the rotation invariant moment. In order to reduce rounding errors of the transform from the Polar coordinate system to the Cartesian coordinate system, a new transformation method is presented and discussed in detail at the same time. The new method constructs a $9\times 9$ shrunk template to transform the Cartesian coordinate system back to the Polar coordinate system. It can reduce transform errors to a much greater degree. Forgery detection, such as copy-move image forgery detection, is a difficult procedure, but experiments prove our method is a great improvement in detecting and identifying forgery images affected by the rotated transform.

The most important decision in cross-docking design is the number of unloading and loading doors. This paper focuses on the design issues of unloading and loading doors of symmetric-I-shaped (I-LTL) cross-docks pervasive in the Chinese auto-part supplying chain which is obviously a very complex system. First of all, this paper analyzes the operation process of I-LTL cross-docking in detail and completes the construction of discrete event simulation that conforms to I-LTL cross-docking operation on the basis of practical details in reality through ARENA platform. In the simulation analysis, this paper selects the physical flow of parts (supporting for arrival frequency and loading capacity of transport vehicles) and I-LTL cross-docking as the simulation experimental factors and applies multilevel factorial design to carry out a large-scale simulation experiment. The results suggest that the required number of receiving dock doors is determined by the arrival frequency of storage vehicles and loading capacity. Moreover, the effect of arrival frequency index is far greater than the loading capacity index. On the other hand, the required number of shipping dock doors primarily depends on the cross-docking consolidation rate and vehicle arrival frequency. Moreover, the index action of consolidation rate is greater than the effect of arriving frequency linearity.

The aim of the present paper is to study conditions under which all the nonwandering points are periodic points, for a discrete dynamical system of two variables defined on a compact manifold. We include a survey of known results in all dimensions, and study the remaining open question in dimension two. We present two results, one negative and one positive. The negative result: we construct a Kupka–Smale diffeomorphism in ${ℝ}^2$ (which can be extended to a diffeomorphism of the sphere) with a closed set of periodic points that differs from the set of nonwandering points. The positive result: we present a condition on the widely studied Hénon family which guarantees that all nonwandering points are periodic. Finally, we close by describing what future work may be needed to resolve our broad goals.

In this paper, a nonclassical nonautonomous diffusion equation with delay is analyzed. First, the well-posedness and the existence of a local solution is proved by using a fixed point theorem. Then, the existence of solutions defined globally in future is ensured. The asymptotic behavior of solutions is analyzed within the framework of pullback attractors as it has revealed a powerful theory to describe the dynamics of nonautonomous dynamical systems. One difficulty in the case of delays concerns the phase space that one needs to construct the evolution process. This yields the necessity of using a version of the Ascoli–Arzelà theorem to prove the compactness.

In this paper, we prove the convergence of the numerical approximations of a scalar parabolic equation modeling a non-Newtonian fluid. We use finite-difference schemes and the well-known method of external approximations.

A Brain Computer Interface (BCI) system is a tool not requiring any muscle action to transmit information. Acquisition, preprocessing, feature extraction (FE), and classification of electroencephalograph (EEG) signals constitute the main steps of a motor imagery BCI. Among them, FE becomes crucial for BCI, since the underlying EEG knowledge must be properly extracted into a feature vector. Linear approaches have been widely applied to FE in BCI, whereas nonlinear tools are not so common in literature. Thus, the main goal of this paper is to check whether some Hurst exponent and fractal dimension based estimators become valid indicators to FE in motor imagery BCI. The final results obtained were not optimal as expected, which may be due to the fact that the nature of the analyzed EEG signals in these motor imagery tasks were not self-similar enough.

By using the reduction technique to impulsive differential equations [Akhmet & Turan, 2006], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li–Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.

In this paper, we analyze the periodic structure of the anisotropic Kepler problem with the same type of perturbations using symplectic Delaunay coordinates and averaging theory. Moreover, sufficient conditions for existence and kind of stability of this class of perturbed Kepler problems are given.

The objective of the present paper is to focus on the problem of the normalization of a Hamiltonian system via the elimination of angle variables involved using the Lie transform technique. The algorithm that we construct assumes that the Hamiltonian is periodic in $n$ angle variables, with two rates: fast and slow. If the angle variables have the same rate only one transformation is required. The equations needed to evaluate the elements of each transformation and the secular perturbations are constructed.

The aim of this paper is to investigate properties of the Weierstrass points on the family of compact Riemann surfaces $C_{a,b,c}:X^4+Y^4+Z^4+a{X}^2{Y}^2+b{X}^2{Z}^2+c{Y}^2{Z}^2=0$, where $a,b$ and $c$ are parameters such that $a^2,b^2,c^2\ne 1,4$ and $a^2+b^2+c^2-abc-4\ne 0,$ by using finite group actions on this family. Furthermore, the geometry of these points is discussed.

In the high-speed railway wireless communication, a joint channel estimation and signal detection algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) system without cyclic prefix in the doubly-selective fading channels. Our proposed method first combines the basis expansion model (BEM) and the inter symbol interference (ISI) cancellation to overcome the situation that exists with the fast time-varying channel and the normalized maximum multipath channel exceeding the length of the cyclic prefix (CP). At first, the channel estimation and signal detection can be approximated without considering the ISI. Then, the channel parameters and signal detection are updated through ISI cancellation and circular convolution reconstruction from the frequency domain. The simulations show the algorithm can improve the performance of channel estimation and signal detection.

Facing many problems of the urban–rural resident pension insurance system in China, one should firstly make sure that this system can be optimized. This paper, based on the modern control theory, sets up differential equations as models to describe the urban–rural resident pension insurance system, and discusses the globally asymptotic stability in the sense of Liapunov for the urban–rural resident pension insurance system in the new equilibrium point. This research sets the stage for our further discussion, and it is theoretically important and convenient for optimizing the urban–rural resident pension insurance system.

In order to avoid the inherent deficiencies of the traditional BP neural network, such as slow convergence speed, that easily leading to local minima, poor generalization ability and difficulty in determining the network structure, the dynamic self-adaptive learning algorithm of the BP neural network is put forward to improve the function of the BP neural network. The new algorithm combines the merit of principal component analysis, particle swarm optimization, correlation analysis and self-adaptive model, hence can effectively solve the problems of selecting structural parameters, initial connection weights and thresholds and learning rates of the BP neural network. This new algorithm not only reduces the human intervention, optimizes the topological structures of BP neural networks and improves the network generalization ability, but also accelerates the convergence speed of a network, avoids trapping into local minima, and enhances network adaptation ability and prediction ability. The dynamic self-adaptive learning algorithm of the BP neural network is used to forecast the total retail sale of consumer goods of Sichuan Province, China. Empirical results indicate that the new algorithm is superior to the traditional BP network algorithm in predicting accuracy and time consumption, which shows the feasibility and effectiveness of the new algorithm.

This paper introduces the capacitated vehicle routing problem with recycling in reverse logistics, and designs a food chain algorithm for it. Some illustrative examples are selected to conduct simulation and comparison. Numerical results show that the performance of the food chain algorithm is better than the genetic algorithm, particle swarm optimization as well as quantum evolutionary algorithm.

A modularized design for the radio frequency (RF) link in automatic test system of multimode mobile communication base station is presented, considering also the characteristics of wireless communication indices and composition of signals of base stations. The test link is divided into general module, time division duplex (TDD) module, module of spurious noise filter, module of downlink intermodulation, module of uplink intermodulation and uplink block module. The composition of modules and link functions are defined, and the interfaces of the general module and the module of spurious noise filter are described. Finally, the estimated gain budget of the test link is presented. It is verified by experiments that the system is reliable and the test efficiency is improved.

In this paper, a novel discrete differential evolution (DDE) algorithm is proposed to solve the vehicle routing problems (VRP) in B2C e-commerce, in which VRP is modeled by the incomplete graph based on the actual urban road system. First, a variant of classical VRP is described and a mathematical programming model for the variant is given. Second, the DDE is presented, where individuals are represented as the sequential encoding scheme, and a novel reparation operator is employed to repair the infeasible solutions. Furthermore, a FLOYD operator for dealing with the shortest route is embedded in the proposed DDE. Finally, an extensive computational study is carried out in comparison with the predatory search algorithm and genetic algorithm, and the results show that the proposed DDE is an effective algorithm for VRP in B2C e-commerce.

Ontology, a model of knowledge representation and storage, has had extensive applications in pharmaceutics, social science, chemistry and biology. In the age of “big data”, the constructed concepts are often represented as higher-dimensional data by scholars, and thus the sparse learning techniques are introduced into ontology algorithms. In this paper, based on the alternating direction augmented Lagrangian method, we present an ontology optimization algorithm for ontological sparse vector learning, and a fast version of such ontology technologies. The optimal sparse vector is obtained by an iterative procedure, and the ontology function is then obtained from the sparse vector. Four simulation experiments show that our ontological sparse vector learning model has a higher precision ratio on plant ontology, humanoid robotics ontology, biology ontology and physics education ontology data for similarity measuring and ontology mapping applications.

We propose a new primal-dual interior-point predictor–corrector algorithm in Ai and Zhang’s wide neighborhood for solving monotone linear complementarity problems (LCP). Based on the understanding of this neighborhood, we use two new directions in the predictor step and in the corrector step, respectively. Especially, the use of new corrector direction also reduces the duality gap in the corrector step, which has good effects on the algorithm’s convergence. We prove that the new algorithm has a polynomial complexity of $O(\sqrt{n}L)$, which is the best complexity result so far. In the paper, we also prove a key result for searching for the best step size along some direction. Considering local convergence, we revise the algorithm to be a variant, which enjoys both complexity of $O(\sqrt{n}L)$ and Q-quadratical convergence. Finally, numerical result shows the effectiveness and superiority of the two new algorithms for monotone LCPs.

Performance evaluation of supply chain (SC) is a vital topic in SC management and inherently complex problems with multilayered internal linkages and activities of multiple entities. Recently, various Network Data Envelopment Analysis (NDEA) models, which opened the “black box” of conventional DEA, were developed and applied to evaluate the complex SC with a multilayer network structure. However, most of them are input or output oriented models which cannot take into consideration the nonproportional changes of inputs and outputs simultaneously. This paper extends the Slack-based measure (SBM) model to a nonradial, nonoriented network model named as U-NSBM with the presence of undesirable outputs in the SC. A numerical example is presented to demonstrate the applicability of the model in quantifying the efficiency and ranking the supply chain performance. By comparing with the CCR and U-SBM models, it is shown that the proposed model has higher distinguishing ability and gives feasible solution in the presence of undesirable outputs. Meanwhile, it provides more insights for decision makers about the source of inefficiency as well as the guidance to improve the SC performance.

In this paper, a method of data flow modeling for a product design process oriented to data parameter is proposed. The data parameters are defined, which are classified as the basic data parameters and complex data parameters. The mechanism of the mapping relationship between different forms of documents and some basic data parameters, and a data transmission based on parameters, are constructed. Aiming at the characteristics of the iterative design process, the parameters version mechanism including node modification and iteration information is proposed. The data parameters transmission relationships are represented by a parameters network model (PNM) based on a directed graph. Finally, through the table of data parameters mapping onto the workflow node and PNM, the data ports and data links in the data flow model are generated automatically by the program. Validation in the 15-meter-diameter S/Ka frequency band antenna design process of the “Reflector, Back frame and Center part design” data flow model shows that the method can effectively shorten the time of data flow modeling and improve the data transmission efficiency.

Due to more severe challenges of traffic safety problems, the Advanced Driver Assistance Systems (ADAS) has received widespread attention. Measuring the distance to a preceding vehicle is important for ADAS. However, the existing algorithm focuses more on straight road sections than on curve measurements. In this paper, we present a novel measuring algorithm for the distance to a preceding vehicle on a curve road using on-board monocular camera. Firstly, the characteristics of driving on the curve road is analyzed and the recognition of the preceding vehicle road area is proposed. Then, the vehicle detection and distance measuring algorithms are investigated. We have verified these algorithms on real road driving. The experimental results show that this method proposed in the paper can detect the preceding vehicle on curve roads and accurately calculate the longitudinal distance and horizontal distance to the preceding vehicle.

A motion object extraction algorithm based on the active contour model is proposed. Firstly, moving areas involving shadows are segmented with the classical background difference algorithm. Secondly, performing shadow detection and coarse removal, then a grid method is used to extract initial contours. Finally, the active contour model approach is adopted to compute the contour of the real object by iteratively tuning the parameter of the model. Experiments show the algorithm can remove the shadow and keep the integrity of a moving object.

This paper presents analytical derivations to study periodic solutions for the two-body problem perturbed by the first zonal harmonic parameter. In particular, three different semianalytical approaches to solve this problem have been studied: (1) the classic perturbation theory, (2) the Lindstedt–Poincaré technique, and (3) the Krylov–Bogoliubov–Mitropolsky method. In addition, the numerical integration by Runge–Kutta algorithm is established. However, the numerical comparison tests show that by increasing the value of angular momentum the solutions provided by Lindstedt–Poincaré and Krylov–Bogoliubov–Mitropolsky methods become similar, and they provide almost identical results using a smaller value for the perturbed parameter which quantify the dynamical flattening of the main body, the Krylov–Bogoliubov–Mitropolsky provides more accurate results to design elliptical periodic solutions than Lindstedt–Poincaré technique when the perturbed parameter has a relatively large value, regardless of the value of angular momentum. This study can be applied to equatorial orbits to obtain closed-form analytical solutions.