A Chaotic Block Encryption Scheme Based on the Piecewise Nonlinear Map

In order to improve communication security, proposed a chaotic block cryptographic scheme based on the coupled piecewise nonlinear map. Using the coupled chaotic systems to generate random binary sequences, a key-dependent shill approach permated the plain-text block and then using the classical chaotic masking technique encrypted the plain-text block. Simulation results show that the proposed algorithm has excellent cryptographic properties such as diffusion and confusion properties and it can resist the know plaintext attacks and chosen plain-text attacks.

Convergence Properties of Piecewise Power Approximations

We address the problem of convergence of approximations obtained from two versions of the piecewise power-law representations arisen in Systems Biology. The most important cases of mean-square and uniform convergence are studied in detail. Advantages and drawbacks of the representations as well as properties of both kinds of convergence are discussed. Numerical approximation algorithms related to piecewise power-law representations are described in Appendix.

DECAY OF POSITIVE WAVES OF HYPERBOLIC BALANCE LAWS

Historically, decay rates have been used to provide quantitative and quali- tative information on the solutions to hyperbolic conservation laws. Quantitative results include the establishment of convergence rates for approximating procedures and numer- ical schemes. Qualitative results include the establishment of results on uniqueness and regularity as well as the ability to visualize the waves and their evolution in time. This work presents two decay estimates on the positive waves for systems of hyperbolic and gen- uinely nonlinear balance laws satisfying a dissipative mechanism. The result is obtained by employing the continuity of Glimm-type functionals and the method of generalized characteristics [7, 17, 241.

A generalized approach for implicit time integration of piecewise linear/nonlinear systems

A generalized solution scheme using implicit time integrators for piecewise linear and nonlinear systems is developed.The piecewise linear characteristic has been well‐discussed in previous studies,in which the original problem has been transformed into linear complementarity problems(LCPs)and then solved via the Lemke algorithm for each time step.The proposed scheme,instead,uses the projection function to describe the discontinuity in the dynamics equations,and solves for each step the nonlinear equations obtained from the implicit integrator by the semismooth Newton iteration.Compared with the LCP‐based scheme,the new scheme offers a more general choice by allowing other nonlinearities in the governing equations.To assess its performances,several illustrative examples are solved.The numerical solutions demonstrate that the new scheme can not only predict satisfactory results for piecewise nonlinear systems,but also exhibits substantial efficiency advantages over the LCP‐based scheme when applied to piecewise linear systems.

A ground-limited nonlinear energy sink

The nonlinear energy sink(NES)is outstanding in vibration control for the well-known character of energy targeted transmitting and resonance automatically capturing.To enhance the practicability,this paper proposes a ground-limited NES.The novel design can be encapsulated in a certain box.However,as the vibration region of NES is limited,the control efficiency of it must be considered seriously.Hence,the ground-limited NES is discussed via the analytical method,the simulation method,and especially the experiment in forced vibration.All parameters involved in this study are obtained through the parameter identification based on the experimental platform.The piecewise nonlinearity is fitted into the continuous nonlinearity by the hyperbolic tangent function.Then the harmonic balance method(HBM)is used during the analytical processing to promote the accuracy of the solution.The direct numerical method produces results to verify the analytical method together with the experimental records.The discussion on the control parameters shows that a proper limiting spring can effectively reduce the vibration of the NES while the cost of the control efficiency is small.In a word,this work provides a simple and reliable approach for restricting the NES,which is beneficial to the design of the NES and broadens the application of the NES in engineering.

Asymptotic Behavior of a Discrete-time Network Model of Two Neurons

This paper is concerned with a delay difference systems arising from an arti-ficial network model of two neurons with piecewise coustant nonlinearity. The differencesystems can be regarded as the discrete analog of the artificial neural network of twoncurons. Some interesting results are obtained for the asymptotic behavior of solutionsof the systems.