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. 本书主要讨论不同类型的自治和非自治不连续微分方程中的分岔.那些具有跳跃的微分方程既可以是右端点不连续的,也可以是在轨迹上不连续,或是方程解的区间常数近似的.本书的结果可以应用于各个领域,如神经网络,脑动力学,机械系统,天气现象,人口动力学等.毫无疑问,分岔理论应该进一步发展到不同类型的微分方程.读者将从本书了解到该理论的最新成果,学会如何将该理论应用到不同类型的不连续微分方程的具体方法.此外,读者将学习到分析这些方程的非自治分岔情况的最新方法

duxiu/initial_release/自治和非自治不连续微分方程中的分岔_40940833.zip

zlibzh/no-category/ARDAK KASHKYNBAYEV, 阿克梅特 (Akhmet, Marat), Marat Akhmet/自治和非自治不连续微分方程中的分岔=BIFURCATION IN AUTONOMOUS AND NONAUTONOMOUS DIFFERENTIAL EQUATIONS WITH DISCONTINUITIES,MARAT AKHMET_116553448.pdf

Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities (Nonlinear Physical Science)

自治和非自治不连续微分方程中的分岔 = Bifurcation in autonomous and nonautonomous differential equations with discontinuities

Bifurcation in autonomous and nonautonomous differential equations with discontinuities = 自治和非自治不连续微分方程中的分岔

Akhmet, Marat, Kashkynbayev, Ardak

Marat Akhmet; Ardak Kashkynbayev

Springer Science + Business Media Singapore Pte Ltd

Springer Singapore Imprint : Springer

Springer Singapore Pte. Limited

Higher Education Press

Springer Nature

Nonlinear physical science, Di 1 ban, Beijing Shi, 2017

Nonlinear Physical Science, Singapore, 2017

Place of publication not identified, 2017

Springer Nature, Singapore, 2017

China, People's Republic, China

Singapore, Singapore

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This book is devoted to bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types. That is, those with jumps present either in the right-hand-side or in trajectories or in the arguments of solutions of equations. The results obtained in this book can be applied to various fields such as neural networks, brain dynamics, mechanical systems, weather phenomena, population dynamics, etc. Without any doubt, bifurcation theory should be further developed to different types of differential equations. In this sense, the present book will be a leading one in this field. The reader will benefit from the recent results of the theory and will learn in the very concrete way how to apply this theory to differential equations with various types of discontinuity. Moreover, the reader will learn new ways to analyze nonautonomous bifurcation scenarios in these equations. The book will be of a big interest both for beginners and experts in the field. For the former group of specialists, that is, undergraduate and graduate students, the book will be useful since it provides a strong impression that bifurcation theory can be developed not only for discrete and continuous systems, but those which combine these systems in very different ways. The latter group of specialists will find in this book several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impacts, differential equations with piecewise constant arguments of generalized type and Filippov systems. A significant benefit of the present book is expected to be for those who consider bifurcations in systems with impulses since they are presumably nonautonomous systems

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.
Erscheinungsdatum: 31.01.2017

2024-06-13