Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities write by Marat Akhmet. This book was released on 2017-01-23. Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities available in PDF, EPUB and Kindle. This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types – those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied to various fields, such as neural networks, brain dynamics, mechanical systems, weather phenomena and population dynamics. Developing bifurcation theory for various types of differential equations, the book is pioneering in the field. It presents the latest results and provides a practical guide to applying the theory to differential equations with various types of discontinuity. Moreover, it offers new ways to analyze nonautonomous bifurcation scenarios in these equations. As such, it shows undergraduate and graduate students how bifurcation theory can be developed not only for discrete and continuous systems, but also for those that combine these systems in very different ways. At the same time, it offers specialists several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impact, differential equations with piecewise constant arguments of generalized type and Filippov systems.
Stability and Bifurcation Theory for Non-Autonomous Differential Equations
Stability and Bifurcation Theory for Non-Autonomous Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stability and Bifurcation Theory for Non-Autonomous Differential Equations write by Anna Capietto. This book was released on 2012-12-14. Stability and Bifurcation Theory for Non-Autonomous Differential Equations available in PDF, EPUB and Kindle. This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.
Functional Analysis in Interdisciplinary Applications—II
Functional Analysis in Interdisciplinary Applications—II - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Functional Analysis in Interdisciplinary Applications—II write by Allaberen Ashyralyev. This book was released on 2021-07-03. Functional Analysis in Interdisciplinary Applications—II available in PDF, EPUB and Kindle. Functional analysis is an important branch of mathematical analysis which deals with the transformations of functions and their algebraic and topological properties. Motivated by their large applicability to real life problems, applications of functional analysis have been the aim of an intensive study effort in the last decades, yielding significant progress in the theory of functions and functional spaces, differential and difference equations and boundary value problems, differential and integral operators and spectral theory, and mathematical methods in physical and engineering sciences. The present volume is devoted to these investigations. The publication of this collection of papers is based on the materials of the mini-symposium "Functional Analysis in Interdisciplinary Applications" organized in the framework of the Fourth International Conference on Analysis and Applied Mathematics (ICAAM 2018, September 6–9, 2018). Presenting a wide range of topics and results, this book will appeal to anyone working in the subject area, including researchers and students interested to learn more about different aspects and applications of functional analysis. Many articles are written by experts from around the world, strengthening international integration in the fields covered. The contributions to the volume, all peer reviewed, contain numerous new results. This volume contains four different chapters. The first chapter contains the contributed papers focusing on various aspects of the theory of functions and functional spaces. The second chapter is devoted to the research on difference and differential equations and boundary value problems. The third chapter contains the results of studies on differential and integral operators and on the spectral theory. The fourth chapter is focused on the simulation of problems arising in real-world applications of applied sciences.
Nonautonomous Bifurcation Theory
Nonautonomous Bifurcation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonautonomous Bifurcation Theory write by Vasso Anagnostopoulou. This book was released on 2023-05-31. Nonautonomous Bifurcation Theory available in PDF, EPUB and Kindle. Bifurcation theory is a major topic in dynamical systems theory with profound applications. However, in contrast to autonomous dynamical systems, it is not clear what a bifurcation of a nonautonomous dynamical system actually is, and so far, various different approaches to describe qualitative changes have been suggested in the literature. The aim of this book is to provide a concise survey of the area and equip the reader with suitable tools to tackle nonautonomous problems. A review, discussion and comparison of several concepts of bifurcation is provided, and these are formulated in a unified notation and illustrated by means of comprehensible examples. Additionally, certain relevant tools needed in a corresponding analysis are presented.
Almost Periodicity, Chaos, and Asymptotic Equivalence
Almost Periodicity, Chaos, and Asymptotic Equivalence - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Almost Periodicity, Chaos, and Asymptotic Equivalence write by Marat Akhmet. This book was released on 2019-06-20. Almost Periodicity, Chaos, and Asymptotic Equivalence available in PDF, EPUB and Kindle. The central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis. Prof. Akhmet's lucid and rigorous examination proves these oscillations are a "regular" component of chaotic attractors. The book focuses on almost periodic functions, first of all, as Stable (asymptotically) solutions of differential equations of different types, presumably discontinuous; and, secondly, as non-isolated oscillations in chaotic sets. Finally, the author proves the existence of Almost Periodic Oscillations (asymptotic and bi-asymptotic) by asymptotic equivalence between systems. The book brings readers' attention to contemporary methods for considering oscillations as well as to methods with strong potential for study of chaos in the future. Providing three powerful instruments for mathematical research of oscillations where dynamics are observable and applied, the book is ideal for engineers as well as specialists in electronics, computer sciences, robotics, neural networks, artificial networks, and biology. Distinctively combines results and methods of the theory of differential equations with thorough investigation of chaotic dynamics with almost periodic ingredients; Provides all necessary mathematical basics in their most developed form, negating the need for any additional sources for readers to start work in the area; Presents a unique method of investigation of discontinuous almost periodic solutions in its unified form, employed to differential equations with different types of discontinuity; Develops the equivalence method to its ultimate effective state such that most important theoretical problems and practical applications can be analyzed by the method.
