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An introduction to discrete-valued time series
A much-needed introduction to the field of discrete-valued time series, with a focus on count-data time series Time series analysis is an essential tool in a wide array of fields, including business, economics, computer science, epidemiology, finance, manufacturing and meteorology, to name just a few. Despite growing interest in discrete-valued time series—especially those arising from counting specific objects or events at specified times—most books on time series give short shrift to that increasingly important subject area. This book seeks to rectify that state of affairs by providing a much needed introduction to discrete-valued time series, with particular focus on count-data time series. The main focus of this book is on modeling. Throughout numerous examples are provided illustrating models currently used in discrete-valued time series applications. Statistical process control, including various control charts (such as cumulative sum control charts), and performance evaluation are treated at length. Classic approaches like ARMA models and the Box-Jenkins program are also featured with the basics of these approaches summarized in an Appendix. In addition, data examples, with all relevant R code, are available on a companion website. • Provides a balanced presentation of theory and practice, exploring both categorical and integer-valued series • Covers common models for time series of counts as well as for categorical time series, and works out their most important stochastic properties • Addresses statistical approaches for analyzing discrete-valued time series and illustrates their implementation with numerous data examples • Covers classical approaches such as ARMA models, Box-Jenkins program and how to generate functions • Includes dataset examples with all necessary R code provided on a companion website An Introduction to Discrete-Valued Time Series is a valuable working resource for researchers and practitioners in a broad range of fields, including statistics, data science, machine learning, and engineering. It will also be of interest to postgraduate students in statistics, mathematics and economics.
eBook
The Fractional Discrete Predator–Prey Model: Chaos, Control and Synchronization
This paper describes a new fractional predator–prey discrete system of the Leslie type. In addition, the non-linear dynamics of the suggested model are examined within the framework of commensurate and non-commensurate orders, using different numerical techniques such as Lyapunov exponent, phase portraits, and bifurcation diagrams. These behaviours imply that the fractional predator–prey discrete system of Leslie type has rich and complex dynamical properties that are influenced by commensurate and incommensurate orders. Moreover, the sample entropy test is carried out to measure the complexity and validate the presence of chaos. Finally, nonlinear controllers are illustrated to stabilize and synchronize the proposed model.
Journal Article
Modeling and simulation of discrete-event systems
This book provides a comprehensive, systematic treatment of discrete event systems modeling and simulation, covering the five major breakthrough areas in modeling over the past sixty years, and integrating these areas into engineering s most widely used modeling and simulation systems.
eBook
A new spatiotemporal chaotic system based on two-dimensional discrete system
Chaos maps are widely used in information security due to some attractive properties, but many low-dimensional chaotic maps have several disadvantages such as small parameter space, small Lyapunov exponent, and long calculation time. To better remedy these problems, the paper presents a new spatiotemporal chaotic system with high complex dynamical behavior and good randomness, which is called the general two-dimensional Hénon map (GTDHM). We mathematically investigate the Lyapunov exponent and spatial dynamical behavior of the new system and give the corresponding theorems and corollaries which reflects the good chaotic performance of the proposed system. Moreover, a novel pseudo-random sequence generator based on GTDHM is investigated, and the statistical testes are performed with NIST SP 800-22 statistical test suite. We explicitly show that pseudo-random sequences generated by GTDHM are random and have a weak correlation and possess a larger parameter space, which are good theoretical guarantees for the security of its application in encryption.
Journal Article
Enhancing the emergence of hyperchaos using an indirect coupling and its verification based on digital implementation
In this work, an indirect coupling used in a pair of simple autonomous discrete systems in order to enhance the emergence of hyperchaos is presented. The peculiarity that the used systems will never generate chaotic or hyperchaotic dynamics by itself makes this case an interesting problem to address. Moreover, it is possible to achieve in-phase or anti-phase synchronization by varying some parameters of the indirect coupling. Additionally, different methods to analyze the emerging dynamics of the coupled systems using an indirect coupling compared to a conventional coupling are presented. Finally, an electronic digital implementation is conducted by using the SPI protocol of two coupled PIC-24FJ64GA006 16-bit microcontrollers.
Journal Article
Asymptotic stability and stabilisation of uncertain delta operator systems with time-varying delays
This study focuses on the asymptotic stability and stabilisation of uncertain linear systems with time-varying delays via delta operator approach. By employing a new model formulation, the time-delayed delta operator system is transformed into an interconnected system for which the uncertainties can become easy to deal with. Based on a two-term approximation of delayed state and scaled small gain theorem, new delay-dependent sufficient conditions of robust asymptotic stability and state-feedback stabilisation of an uncertain delta operator time-delayed system are established by using a novel Lyapunov–Krasovskii functional. The criteria obtained unify some previously suggested relevant methods seen in literature for achieving asymptotic stability and stabilisation of both continuous and discrete systems into the delta operator framework. Numerical examples presented explicitly demonstrate the advantages and effectiveness of the proposed methods.
Journal Article
Asymptotic behavior of solutions of nonlinear discrete systems in critical cases
The paper is dedicated to the analysis of the asymptotic behavior of essentially nonlinear discrete systems whose linearization possesses eigenvalues on the unit circle. For these systems, the paper establishes sufficient conditions for the asymptotic stability regardless of terms higher than the third order. Moreover, it derives an asymptotic stability criterium for a reduced critical subsystem. The proof incorporates a constructive approach for deriving Lyapunov functions using the center manifold reduction and normal form method. The key result of the paper asserts that, given the obtained stability conditions, the solutions of the system converge to the origin with a polynomial decay rate. The paper also introduces a method for evaluating the coefficients of the decay rate estimate. To illustrate these findings, we apply the obtained result to analyzing nonlinear business cycle and predator-pray models.
Journal Article
Trajectory Controllability for Delayed Linear Discrete Systems with Second-Order Differences
In this paper, we investigate the trajectory controllability of second order delayed discrete systems, aided by the representation of the solution. By employing two delayed discrete matrix functions, we establish sufficient and necessary conditions for Kalman-type controllability criterion in general case and special case. Examples are provided to illustrate the effectiveness of our theoretical results.
Journal Article