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VALUE DISTribution OF MEROMORPHIC SOLUTIONS OF CERTAIN NON-LINEAR DIFFERENCE EQUATIONS

Acta Mathematica Scientia 2019年第4期39卷 1173-1184页

作者： Minfeng CHEN Zongsheng GAO Jilong ZHANG School of Mathematics and Statistics Guangdong University of Foreign Studies Guangzhou 510006 China LMIB and School of Mathematics and Systems Science Beihang University Beijing 100191 China

In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.

关键词： Non-linear difference equation meromorphic solution rational solution value dist ribution

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Message delay time distribution analysis for controller area network under errors

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Frontiers of Information Technology & Electronic Engineering 2019年第6期20卷 760-772页

作者： Lei-ming ZHANG Yi-chao SUN Yong LEI State Key Laboratory of Fluid Power & Mechatronic Systems Zhejiang University Hangzhou 310027 China

Controller area network(CAN) is a widely used fieldbus protocol in various industrial *** understand the network behavior under errors for the optimal design of networked control systems, the message response time of the CAN network needs to be analyzed. In this study, a novel delay time distribution analysis method for the response messages is proposed when considering errors. In this method the complex message queues are decomposed into typical message patterns and cases. First, a stochastic fault model is developed, and the probability factor is defined to calculate the error distribution. Then the message delay time distribution for the single slave node configuration is analyzed based on the error distribution. Next, based on the delay time distribution analysis of typical patterns and cases, an analysis framework of message delay time distribution for the master/slave configuration is developed. The testbed is constructed and case studies are conducted to demonstrate the proposed methodology under different network configurations. Experimental results show that the delay time distributions calculated by the proposed method agree well with the actual observations.

关键词： Cont roller area network Message delay Probability dist ribution Errors

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