2,312 publications from this institution
This paper discusses topological shadowing property, chain transitivity, total chain transitivity, and chain mixing property for dynamical systems on uniform spaces and characterizes some topological chain properties for dynamical systems on compact uniform spaces. In particular, it is proved that a compact dynamical system is topologically chain mixing if and only if it is totally topologically chain transitive. Moreover, some basic properties of topological shadowing and non-wandering points on uniform spaces are obtained.
In this note, it is shown that there exist two non-syndetically sensitive cascades defined on complete metric spaces whose product is syndetically sensitive, answering negatively the Question 9.2 posed in [12, Miller, A., Money, C., Turk. J. Math., 41 (2017): 1323{1336]. Moreover, it is shown that there exists a syndetically sensitive semiflow (G;X) defined on a complete metric space X such that (G1;X) is not sensitive for some syndetic closed submonoid G1 of G, answering negatively the Open question 3 posed in [13, Money, C., PhD thesis, University of Louisville, 2015] and Question 43 posed in [8, Miller, A., Real Anal. Exchange, 42 (2017): 9{24].
"Did you get the physics right?" This is always a good question for our members of the IEEE Circuits and Systems Society.
Objective To discuss the effect of different antihypertensive programs on blood pressure and left ven-tricular hypertrophy of elderly patients with hypertension, and to provide a guidance for clinical practice. Methods A total of 162 patients with hypertension in Department of Internal Medicine in our hospital were selected from December 2012 to December 2014, and randomly divided into the observation group and the control group according to random number table, with 81 patients in each group. The observation group was treated by amlodipine combined with hydrochlorothi-azide, and the control group was treated with amlodipine combined with irbesartan, for a treatment course of two mouths. The blood pressure, left ventricular mass index (LVMI), after treatment were compared between the two groups. Results Among the 162 patients, eight patients were lost to follow-up. After treatment, the systolic blood pres-sure of patients in observation group and the control group was (123 ± 6) mmHg, (129 ± 8) mmHg, respectively, which were significantly decreased compared with those before treatment [(157 ± 12) mmHg, (156 ± 9) mmHg], and the value was significantly lower in observation group than control group (P<0.05). After treatment, the degree of LVMI were sig-nificantly reduced compared with before treatment, and the LVMI in observation group was significantly lower than that in the control group [(124±18) g/m2 vs (132±16) g/m2, P<0.05]. Conclusion Amlodipine combined with irbesartan and amlodipine combined with hydrochlorothiazide can both reduce blood pressure and LVMI of patients. However, the treat-ment effect of amlodipine combined with hydrochlorothiazide is more significant, which is worthy of clinical populariza-tion and application.
No abstract is provided for this article.
No abstract is provided for this article.
For a compact metric space $ Y $ and a continuous map $ g:Y\rightarrow Y $, the collective accessibility and collectively Kato chaotic of the dynamical system $ (Y, g) $ were defined. The relations between topologically weakly mixing and collective accessibility, or strong accessibility, or strongly Kato chaos were studied. Some common properties of $ g $ and $ \overline{g} $ were given. Where $ \overline{g}: \kappa(Y)\rightarrow \kappa(Y) $ is defined as $ \overline{g}(B) = g(B) $ for any $ B\in\kappa(Y) $, and $ \kappa(Y) $ is the collection of all nonempty compact subsets of $ Y $. Moreover, it is proved that $ g $ is collectively accessible (or strongly accessible) if and only if $ \overline{g} $ in $ w^{e} $-topology is collectively accessible (or strongly accessible).
Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e., globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible and unified chaotification method of designing a general chaotic continuous-time autonomous nonlinear system. For a system consisting of a linear and a nonlinear subsystem, chaotification is achieved using separation of state variables, which decomposes the system into two open-loop subsystems interacting through mutual feedback resulting in an overall closed-loop nonlinear feedback system. Under the condition that the nonlinear feedback control output is uniformly bounded where the nonlinear function is of bounded-input/bounded-output, it is proved that the resulting system is chaotic in the sense of being globally bounded with a required placement of Lyapunov exponents. Several numerical examples are given to verify the effectiveness of the theoretical design. Since linear systems are special cases of nonlinear systems, the new method is also applicable to linear systems in general.
No abstract is provided for this article.
11R19. Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems. - Guanrong Chen (Univ of Houston, Houston TX) and Trung Tat Pham (Univ of Houston, Clear Lake, Houston TX). CRC Press LLC, Boca Raton FL. 2001. 316 pp. ISBN 0-8493-1658-8. $89.95.Reviewed by NM Boustany (GM Tech Center, General Motors Energy Center, Eng Bldg, 30200 Mound Rd, 480-111-S31, Troy MI 48090).In one of the debates of the 2000 presidential campaign, then Candidate George W Bush described Al Gore's analysis of his tax refund proposals as Fuzzy Math. It is not clear whether or not Mr Bush was also taking a jab at the field, or even whether or not he was aware of its existence. At any rate, the popular press as well as TV and radio news shows made a lot of hay with the expression: Fuzzy Math, to the extent that Professor Bart Kosko (a major contributor to the field and author of the popular bestseller Fuzzy Thinking, Hyperion Press, NY, 1993) felt compelled to write a short editorial on the subject for the New York Times that same week. The chances are that control theorists of this reviewer's generation have had to study fuzzy analysis several years after graduating. To this crop of control engineers, fuzzy thinking required quite a paradigm shift. Therefore, the field was not readily accepted and was received, in the early years, with considerable skepticism; all this despite the write-ups in Time Magazine and all the touted successes by Japanese and Korean engineers in their implementations of fuzzy systems. Upon closer scrutiny, these successes did not appear to constitute definitive proof of the superiority of these approaches over the more classical ones. The detractors would always point to a sensor or actuator that had not been used in earlier implementations relying on more conventional techniques. In addition, the claims that the methodology is mathematical model free seemed often exaggerated. Many reports on implementations relied on models for validation. Needless to say, the early years of fuzzy analysis witnessed a polarization of the control community. In recent years, this feud has considerably abated. This could be due to numerous factors such as the Old Guard reaching retirement and the wider acceptance of techniques with the promise of producing "intelligence" and "learning" in control systems. Fuzzy analysis builds on fuzzy logic, which extends the classical logic handed down to us from the early days of Western thinking by Aristotle. In classical logic, something is true or false; there is no in between. An element either belongs to set or to its complement. This "black or white" of classical logic has led to paradoxes. Fuzzy thinking, on the other hand, introduces degrees of grayness, or degrees of belonging to a set. These gray scales have provided possible resolutions to these paradoxes. Quite often these features of fuzzy thinking are compared and likened to elements in Eastern philosophy. This is often cited as the reason why fuzzy thinking has found wider acceptance in the East. Chapters 1 and 2 of this book lay the foundations. After introducing fuzzy logic and fuzzy set theory in Chapter 1, some results from measure theory are presented. The section on measure theory makes for difficult reading and could be relegated to an appendix in future editions. Interval arithmetic is then introduced, and many of the results on interval calculus are presented. This chapter is straightforward mathematically, but is nevertheless tedious to work through. The examples at the end do a good job of clarifying the theory. Chapter 2 takes the reader from classical logic to fuzzy logic via 2-valued and n-valued logic. Again, the examples at the end of the chapter do the reader a great service. Chapter 3 builds on the foundations of Chapters 1 and 2 and develops the idea of fuzzy models moving from static models to dynamic models. The notion of least square parameter identification is extended to fuzzy models. In Chapter 4, fuzzy control is introduced beginning with a discussion of programable logic controllers. This provides a good starting point for the ensuing discussions on model-free and model-based fuzzy control methods. In Chapter 5, PID control is extended to the fuzzy case. Chapter 6 builds on the optimal parameter identification techniques developed earlier and extends notions from adaptive control to the fuzzy case. Chapter 7 discusses several case studies in detail. In some cases, the mathematical development is tedious, especially the one on interval calculus which is crucial to the understanding of the rest of the text. This could be laid out in a more user-friendly way. Also, some ideas are presented without much motivation. One example is the discussion on defuzzification. Various alternatives for defuzzification are presented without much discussion on what these are attempting to do or why one would choose one over the other. The above criticisms point to minor shortcomings that are relatively easy to amend in future editions. Overall, the text is very well written and provides a rigorous analytical approach to fuzzy systems. The topics are laid out in a logical sequence where later chapters build on the ideas of the earlier ones. Solved examples at the end of the chapters do a good job of clarifying the concepts in the body of these chapters. This reviewer recommends Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems either as a textbook on fuzzy control or as a companion reference for a more general course on intelligent control. The book also belongs on the shelves of engineering libraries of both industry and academia.
This paper studies the construction of one-dimensional real chaotic polynomial maps. Given an arbitrary nonzero polynomial of degree m (≥ 0), two methods are derived for constructing chaotic polynomial maps of degree m + 2 by simply multiplying the given polynomial with suitably designed quadratic polynomials. Moreover, for m + 2 arbitrarily given different positive constants, a method is given to construct a chaotic polynomial map of degree 2m based on the coupled-expansion theory. Furthermore, by multiplying a real parameter to a special kind of polynomial, which has at least two different non-negative or nonpositive zeros, the chaotic parameter region of the polynomial is analyzed based on the snap-back repeller theory. As a consequence, for any given integer n ≥ 2, at least one polynomial of degree n can be constructed so that it is chaotic in the sense of both Li–Yorke and Devaney. In addition, two natural ways of generalizing the logistic map to higher-degree chaotic logistic-like maps are given. Finally, an illustrative example is provided with computer simulations for illustration.
This paper studies the $C^1$-perturbation problem of strictly$A$-coupled-expanding maps in finite-dimensional Euclidean spaces, where $A$ is an irreducible transition matrix with one row-sum no less than $2$.It is proved that under certain conditions strictly $A$-coupled-expanding maps are chaotic in the sense of Li-Yorke or Devaney under small $C^1$-perturbations. It is shown that strictly $A$-coupled-expanding maps are $C^1$ structurally stable in their chaotic invariant sets under certain stronger conditions. One illustrative example is provided with computer simulations.
Most classical chaotic systems, such as the Lorenz system and the Chua circuit, have chaotic attractors in bounded regions. This article constructs and analyzes a different kind of non-smooth impulsive systems, which have growing numbers of attractors in the sense that the number of attractors or the scrolls of an attractor is growing as time increases, and these attractors or scrolls are not located in bounded regions. It is found that infinitely many chaotic attractors can be generated in some of such systems. As an application, both theoretical and numerical analyses of an impulsive Lorenz-like system with infinitely many attractors are demonstrated.
