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This paper lists the Preface, Table of Contents, Index of Python Programs and the book Index.
2018
Please cite the published version birkhauser-science.de 1st ed. 2018, XVI, 665 p. 277 illus., 118 illus. in color.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
International Journal of Applied Mathematical Research, 2012
Dynamical system is a young and vigorously growing area of research which promises enormous potential and opportunities. This paper aims to introduce some of the preliminary concepts of dynamical systems. Many application sides of the subject are noted to encourage the reader for future developments. Resources are supplied in the references for further reading.
2010
The aim of this paper is to give an account of some problems considered in past years in the setting of Dynamical Systems, some new research directions and also state some open problems
1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation, 1997
C o 1x1 p u t at i o ii by D y ii alii i c a1 S y s t e 111 s
2017
Mathematica is extremely popular with a wide range of researchers from all sorts of disciplines. It is a symbolic, numerical and graphical manipulation package. In this paper we provide an introduction to the theory of discrete dynamical systems with the aid of the Mathematica for both senior undergraduates and graduate students. Mathematica applications cover the stability of the one dimensional system, the Cobweb diagram for one dimensional system, the time series diagram, the phase plane diagrams for two-dimensional systems. Applications are taken from biomathematics subjects: prey-predator models, host-parasitoid models, population dynamics, and modeling the populations of interacting species, bifurcation, and basin of attractions are given with codes and examples.
Nonlinear Analysis: Theory, Methods & Applications, 1997
Bifurcations and Periodic Orbits of Vector Fields, 1993
We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal-there are many technical details which are not fully discussed. The topics are chosen to demonstrate the various interactions between numerical computation and mathematical theory in the area of dynamical systems. We present an algorithm for the computation of stable manifolds of equilibrium points, describe the computation of Hopf bifurcations for equilibria in parametrized families of vector fields, survey the results of studies of codimension two global bifurcations, discuss a numerical analysis of the Hodgkin and Huxley equations, and describe some of the effects of symmetry on local bifurcation.
ELECTRICAL AND COMPUTER SYSTEMS
In this paper it is considered and generalized hypothesis about existence of 3 classes of processes: physical, mental and mathematical. It is shown that in all nonlinear dynamical systems the key factor in determining their quantitative and qualitative characteristics is the information about fixed points of dynamical systems and their orbit properties.
2007
One approach starts from time-continuous differential equations and leads to time-discrete maps, which are obtained from them by a suitable discretization of time. This path is pursued, eg, in the book by Strogatz [Str94]. 1 The other approach starts from the study of time-discrete maps and then gradually builds up to time-continuous differential equations, see, eg,[Ott93, All97, Dev89, Has03, Rob95].
2012
, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a cantor set-one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.
An introduction to dynamical systems
Abstract These are easy-to-read lecture notes for a short first-year Ph. D. student course on Applied Dynamical Systems, given at the London Taught Course Centre in Spring 2008, 2009 and 2010. The full course consists of two parts, covering four and six hours of lectures, respectively. The first part taught by Wolfram Just is on Basic Dynamical Systems. The present notes cover only the second part, which leads From Deterministic Chaos to Deterministic Diffusion.
Akademos : Revista de Ştiinţă, Inovare, Cultură şi Artă, 2022
State university of Moldova sistemele dinamice neautonome şi aPlicațiile lor rezumat. Articolul reprezintă o scurtă trecere în revistă a cercetărilor efectuate de autor în ultimii 10-15 ani privind sistemele dinamice neautonome și aplicațiile acestora. Sistemele dinamice neautonome constituie un nou domeniu ce contribuie la dezvoltarea rapidă a matematicii (teoria sistemelor dinamice). Mii de articole, inclusiv zeci de articole de sinteză și un șir de monografii despre sistemele dinamice neautonome au fost publicate în ultimele decenii, iar problematica respectivă a făcut cap de afiș la conferințele internaționale. Autorul a publicat trei monografii pe problema sistemelor dinamice neautonome. În acest articol este oferită o prezentare generală a rezultatelor obținute. Cuvinte-cheie: soluții periodice, soluții cvasi-periodice, soluții aproape periodice Bohr/Levitan, soluții Bohr aproape automorfe, soluții recurente Birkhoff, soluții stabile Lagrange, soluții aproape recurente, soluții stabile Poisson, stabilitate Lyapunov, stabilitate asimptotică, atractori globali. summary. This article is devoted to a brief overview of the author's works over the past 10-15 years on non-autonomous dynamic systems and their applications. Non-autonomous dynamical systems are a new and rapidly developing field of mathematics (theory of dynamical systems). Thousands of articles, dozens of reviews and a number of monographs on non-autonomous dynamic systems and their applications have been published over the past 10-15 years. Special international conferences and scientific journals are dedicated to them. My results on non-autonomous dynamical systems and their applications are published in three monographs. In this article, we provide an overview of these results.
Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, 2017
Ordinary differential equations arise in a variety of applications, including e.g. climate systems, and can exhibit complicated dynamical behaviour. Complete Lyapunov functions can capture this behaviour by dividing the phase space into the chain-recurrent set, determining the long-time behaviour, and the transient part, where solutions pass through. In this paper, we present an algorithm to construct complete Lyapunov functions. It is based on mesh-free numerical approximation and uses the failure of convergence in certain areas to determine the chain-recurrent set. The algorithm is applied to three examples and is able to determine attractors and repellers, including periodic orbits and homoclinic orbits.
Nonlinear Control Systems Design 1992, 1993
Control systems Call be viewed as dynamical systems over (infmite)• dimensional state spaces. From this point of view the long tenn behavior of control systems, such as limit sets, Mone sets. approximations on the entire time axis, ergodicity, Lyapunov exponents, stable and unstable manifolds etc. becomes accessible. This paper presents some of the underlying theory, as well as applications 1.0 the global characterization of control systems with bounded control range that are not completely controllable, to control of chaotic systems, and to exponential stability of uncertain systems.
Iconic Research And Engineering Journals, 2018
In this paper, we discuss some applications of exciting fields like Mathematics, Statistics, Medical, Biological Sciences, Engineering, Economics etc. We show their real-life applications both theoretically and analytically considering some phenomena of the nature. We mainly focused on some applications of dynamical system in real life cases known as chaos, iteration, fractal geometry, Mandelbrot and Julia sets. We derive some mathematical formula concerning dynamical systems. Necessary programs are considered for all cases. We use Mathematica and MATLAB to perform programming.
Journal of the Institute of Engineering
Dynamical system is a mathematical formalization for any fixed rule that is described in time dependent fashion. The time can be measured by either of the number systems - integers, real numbers, complex numbers. A discrete dynamical system is a dynamical system whose state evolves over a state space in discrete time steps according to a fixed rule. This brief survey paper is concerned with the part of the work done by José Sousa Ramos [2] and some of his research students. We present the general theory of discrete dynamical systems and present results from applications to geometry, graph theory and synchronization. Journal of the Institute of Engineering, 2018, 14(1): 35-51
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