Zayıf sinyal tespit uygulamalarına yönelik yeni kaotik sistem geliştirme yaklaşımı

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Bu tez çalışmasında, zayıf sinyal tespit uygulamaları için özgün kaotik sistem geliştirmeye yönelik yeni bir yaklaşım sunulmuştur. Önerilen kaos tabanlı zayıf sinyal tespit yöntemi literatürdeki standart zayıf sinyal tespit yöntemlerinden farklıdır. Bu yolla, farklı frekans değerlerinde tespit yapmaya uygun iki yeni kaotik sistem bulunmuştur. Tezde, yeni geliştirilen yöntem kullanılarak elde edilen iki özgün kaotik osilatör tanıtılmıştır. Bu sistemler basit yapılı olup, parametrik çeşitliliğe ve yüksek uygulanabilme kapasitesine sahiptir. Yeni sistemlerin dinamik karakteristikleri detaylı olarak incelenmiştir. Bununla beraber, Duffing-Holmes, Van Der Pol ve iki hiperkaotik Lorenz sisteminin de dinamik karakteristikleri detaylı olarak incelenmiştir. İlk olarak, sistemlerin Lyapunov metodu ile analizleri yapılmıştır. Sistemlerin durumu ile sürülme teriminin genliği arasındaki ilişki Lyapunov üstellerinin incelenmesi ile ortaya çıkarılmıştır. Kaotik sistemlerin dinamik davranışları bu yolla gözlemlenmiştir. İkinci olarak, kaotik sistemlerin kritik eşik değeri çatallaşma analizi yapılarak tespit edilmiştir. Tanjant çatallaşma noktası adı verilen bu nokta, güçlü gürültü altındaki zayıf sinyal bilgisinin tespiti için en uygun noktadır. Bununla beraber, yeni kaotik sistemlerin elektronik devreleri tasarlanarak benzetimleri de yapılmıştır. Son olarak önerilen sistemlerin zayıf sinyal tespit uygulamaları yapılmıştır. Benzetim sonuçları, sistemlerin yüksek doğrulukta ve düşük değerli sinyal gürültü oranı (SGO) ile zayıf sinyal tespiti yapabildiğini göstermiştir. Bununla beraber bu sistemler, yüksek frekans değerlerinde de tespit yapabilmektedir. Duffing-Holmes, Van Der Pol ve iki hiperkotik Lorenz sisteminin de zayıf sinyal tespit uygulamaları yapılmıştır. Matlab-Simulink® ve OrCAD-PSpice® ortamlarında gerçekleştirilen benzetim çalışmalarının sonuçları, çalışılan sistemlerin teorik analizlerinin doğru olduğunu göstermiştir. Yeni yöntemle geliştirilen özgün kaotik sistemler, endüstriyel metal malzemeleri tahribatsız muayene eden cihazlar, metal dedektörler, elektromanyetik akustik transdüserler gibi cihazların zayıf yankı sinyallerinin tespitinde kullanılabilecek potansiyel sistemlerdir.In this thesis, a new approach to improve novel chaotic systems for weak signal detection applications is presented. The new weak signal detection method based on chaos is different from standart weak signal detection metod in the literature. Two novel chaotic systems, which are suitable for high level weak signal detection applications, are improved by this way. In the thesis, two novel sinusoidal attractors, which are improved by the new metod, are presented. These new systems have simple stracture, parametric variety and high applicability. Dynamic characteristics of the novel systems are studied detailed. Furthermore, dynamic characteristics of Duffing-Holmes, Van Der Pol and two hyperchaotic Lorenz systems are also studied. Firstly, the relationship between the system state and amplitude of the forcing term is defined by examining the Lyapunov exponents of the systems. Dynamical behaviors of these chaotic systems are observed by this way. Secondly, the critical threshold values of these chaotic systems are determined by the bifurcation analysis. This critical value named as critical bifurcation point is a suitable one to detect weak signal which is submerged in strong noise. Furthermore, electronic circuits of the novel chaotic attractors are designed and simulated. Finally, weak signal detection applications of the novel systems are studied. Simulation results indicate that these novel systems can detect weak signal with high detection accuracy and low signal to noise ratio (SNR). These systems can also detect weak signal in high frequencies. Weak signal detection applications of Duffing-Holmes, Van Der Pol and two hyperchaotic Lorenz systems are also studied. Matlab-Simulink® and OrCAD-PSpice® simulation results prove the correctness of the theorycal analysis of studied systems. These improved novel systems are potential sistems to detect weak echo signals, which are non-destructive detection devices of industrial metal materials, metal detectors and electromagnetic acustic transducers

Models of self-organization in biological development

Bibliography: p. 297-320.In this thesis we thus wish to consider the concept of self-organization as an overall paradigm within which various theoretical approaches to the study of development may be described and evaluated. In the process, an attempt is made to give a fair and reasonably comprehensive overview of leading modelling approaches in developmental biology, with particular reference to self-organization. The work proceeds from a physical or mathematical perspective, but not unduly so - the major mathematical derivations and results are relegated to appendices - and attempts to fill a perceived gap in the extant review literature, in its breadth and attempted impartiality of scope. A characteristic of the present account is its markedly interdisciplinary approach: it seeks to place self-organization models that have been proposed for biological pattern formation and morphogenesis both within the necessary experimentally-derived biological framework, and in the wider physical context of self-organization and the mathematical techniques that may be employed in its study. Hence the thesis begins with appropriate introductory chapters to provide the necessary background, before proceeding to a discussion of the models themselves. It should be noted that the work is structured so as to be read sequentially, from beginning to end; and that the chapters in the main text were designed to be understood essentially independently of the appendices, although frequent references to the latter are given. In view of the vastness of the available information and literature on developmental biology, a working knowledge of embryological principles must be assumed. Consequently, rather than attempting a comprehensive introduction to experimental embryology, chapter 2 presents just a few biological preliminaries, to 'set the scene', outlining some of the major issues that we are dealing with, and sketching an indication of the current status of knowledge and research on development. The chapter is aimed at furnishing the necessary biological, experimental background, in the light of which the rest of the thesis should be read, and which should indeed underpin and motivate any theoretical discussions. We encounter the different hierarchical levels of description in this chapter, as well as some of the model systems whose experimental study has proved most fruitful, some of the concepts of experimental embryology, and a brief reference to some questions that will not be addressed in this work. With chapter 3, we temporarily move away from developmental biology, and consider the wider physical and mathematical concepts related to the study of self-organization. Here we encounter physical and chemical examples of spontaneous structure formation, thermodynamic considerations, and different approaches to the description of complexity. Mathematical approaches to the dynamical study of self-organization are also introduced, with specific reference to reaction-diffusion equations, and we consider some possible chemical and biochemical realizations of self-organizing kinetics. The chapter may be read in conjunction with appendix A, which gives a somewhat more in-depth study of reaction-diffusion equations, their analysis and properties, as an example of the approach to the analysis of self-organizing dynamical systems and mathematically-formulated models. Appendix B contains a more detailed discussion of the Belousov-Zhabotinskii reaction, which provides a vivid chemical paradigm for the concepts of symmetry-breaking and self-organization. Chapter 3 concludes with a brief discussion of a model biological system, the cellular slime mould, which displays rudimentary development and has thus proved amenable to detailed study and modelling. The following two chapters form the core of the thesis, as they contain discussions of the detailed application of theoretical concepts and models, largely based on self-organization, to various developmental situations. We encounter a diversity of models which has arisen largely in the last quarter century, each of which attempts to account for some aspect of biological pattern formation and morphogenesis; an aim of the discussion is to assess the extent of the underlying unity of these models in terms of the self-organization paradigm. In chapter 4 chemical pre-patterns and positional information are considered, without the overt involvement of cells in the patterning. In chapter 5, on the other hand, cellular interactions and activities are explicitly taken into account; this chapter should be read together with appendix C, which contains a brief introduction to the mathematical formulation and analysis of some of the models discussed. The penultimate chapter, 6, considers two other approaches to the study of development; one of these has faded away, while the other is still apparently in the ascendant. The assumptions underlying catastrophe theory, the value of its applications to developmental biology and the reasons for its decline in popularity, are considered. Lastly, discrete approaches, including the recently fashionable cellular automata, are dealt with, and the possible roles of rule-based interactions, such as of the so-called L-systems, and of fractals and chaos are evaluated. Chapter 7 then concludes the thesis with a brief assessment of the value of the self-organization concept to the study of biological development

Нелінійна динаміка — 2013

The book of Proceedings includes extended abstracts of presentations on the Fourth International conference on nonlinear dynamics