Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator

Dynamical degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based cryptosystems. The existing solutions mainly focus on the compensation of dynamical properties rather than on the elimination of the inherent biases of chaotic systems. In this paper, a unidirectional hybrid control method is proposed to improve the dynamical properties and to eliminate the biases of digital chaotic maps. A continuous chaotic system is introduced to provide external feedback control of the given digital chaotic map. Three different control modes are investigated, and the influence of control parameter on the properties of the controlled system is discussed. The experimental results show that the proposed method can not only improve the dynamical degradation of the digital chaotic map but also make the controlled digital system produce outputs with desirable performances. Finally, a pseudorandom number generator (PRNG) is proposed. Statistical analysis shows that the PRNG has good randomness and almost ideal entropy values.     

Electrical Power Diversification: An Approach Based on the Method of Maximum Entropy in the Mean

Electrical energy is generated in different ways, each located at some specific geographical area, and with different impact on the environment. Different sectors require heterogeneous rates of energy delivery, due to economic requirements. An important problem to solve is to determine how much energy must be sent from each supplier to satisfy each demand. Besides, the energy distribution process may have to satisfy ecological, technological, or economic cost constraints.     

Analysis on the Development of Digital Economy in Guangdong Province Based on Improved Entropy Method and Multivariate Statistical Analysis

The lack of adequate indicators in the research of digital economy may lead to the shortage of data support on decision making for governments. To solve this problem, first we establish a digital economy indicator evaluation system by dividing the digital economy into four types: “basic type”, “technology type”, “integration type” and “service type” and select 5 indicators for each type. On this basis, the weight of each indicator is calculated to find the deficiencies in the development of some digital economic fields by the improved entropy method. By drawing on the empowerment idea of Analytic Hierarchy Process, the improved entropy method firstly compares the difference coefficient of indicators in pairs and maps the comparison results to the scales 1–9. Then, the judgment matrix is constructed based on the information entropy, which can solve as much as possible the problem that the difference among the weight of each indicator is too large in traditional entropy method. The results indicate that: the development of digital economy in Guangdong Province was relatively balanced from 2015 to 2018 and will be better in the future while the development of rural e-commerce in Guangdong Province is relatively backward, and there is an obvious digital gap between urban and rural areas. Next we extract two new variables respectively to replace the 20 indicators we select through principal component analysis and factor analysis methods in multivariate statistical analysis, which can retain the original information to the greatest extent and provide convenience for further research in the future. Finally, we and provide constructive comments of digital economy in Guangdong Province from 2015 to 2018.     

Error Analysis of a PFEM Based on the Euler Semi-Implicit Scheme for the Unsteady MHD Equations

In this article, we mainly consider a first order penalty finite element method (PFEM) for the 2D/3D unsteady incompressible magnetohydrodynamic (MHD) equations. The penalty method applies a penalty term to relax the constraint “∇·u=0”, which allows us to transform the saddle point problem into two smaller problems to solve. The Euler semi-implicit scheme is based on a first order backward difference formula for time discretization and semi-implicit treatments for nonlinear terms. It is worth mentioning that the error estimates of the fully discrete PFEM are rigorously derived, which depend on the penalty parameter ϵ, the time-step size τ, and the mesh size h. Finally, two numerical tests show that our scheme is effective.