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Titlebook: Nonlinear Differential Equations and Dynamical Systems; Ferdinand Verhulst Textbook 19901st edition Springer-Verlag Berlin Heidelberg 1990

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樓主
發(fā)表于 2025-3-21 19:52:52 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Nonlinear Differential Equations and Dynamical Systems
編輯Ferdinand Verhulst
視頻videohttp://file.papertrans.cn/668/667391/667391.mp4
叢書名稱Universitext
圖書封面Titlebook: Nonlinear Differential Equations and Dynamical Systems;  Ferdinand Verhulst Textbook 19901st edition Springer-Verlag Berlin Heidelberg 1990
描述On the subject of differential equations a great many elementary books have been written. This book bridges the gap between elementary courses and the research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed. Stability theory is developed starting with linearisation methods going back to Lyapunov and Poincaré. The global direct method is then discussed. To obtain more quantitative information the Poincaré-Lindstedt method is introduced to approximate periodic solutions while at the same time proving existence by the implicit function theorem. The method of averaging is introduced as a general approximation-normalisation method. The last four chapters introduce the reader to relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, Hamiltonian systems (recurrence, invariant tori, periodic solutions). The book presents the subject material from both the qualitative and the quantitative point of view. There are many examples to illustrate the theory and the reader should be able to start doing research
出版日期Textbook 19901st edition
關(guān)鍵詞Implicit function; averaging methods; bifurcation theory; chaos; differential equation; differential equa
版次1
doihttps://doi.org/10.1007/978-3-642-97149-5
isbn_ebook978-3-642-97149-5Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag Berlin Heidelberg 1990
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沙發(fā)
發(fā)表于 2025-3-21 23:50:34 | 只看該作者
Periodic solutions,The concept of a periodic solution of a differential equation was introduced in section 2.3. We have shown that in the case of an autonomous equation the periodic solutions correspond with closed orbits in phase-space.
板凳
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地板
發(fā)表于 2025-3-22 07:37:23 | 只看該作者
Introduction to perturbation theory,This chapter is intended as an introduction for those readers who are not aquainted with the basics of perturbation theory. In that case it serves in preparing for the subsequent chapters.
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發(fā)表于 2025-3-22 09:38:04 | 只看該作者
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發(fā)表于 2025-3-22 14:21:14 | 只看該作者
Relaxation oscillations,Relaxation oscillations are periodic phenomena with very special features during a period. The characteristics can be illustrated by the following mechanical system.
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發(fā)表于 2025-3-22 17:56:09 | 只看該作者
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發(fā)表于 2025-3-23 02:07:13 | 只看該作者
Stability by linearisation,pecial solutions. In section 5.4 we have discussed linearisation and we have given a summary of the analysis of linear systems. These methods have been in use for a long time but only since around 1900 the justification of linearisation methods has been started by Poincaré and Lyapunov.
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發(fā)表于 2025-3-23 06:22:05 | 只看該作者
Stability analysis by the direct method,eceding chapter. When linearising one starts off with small perturbations of the equilibrium or periodic solution and one studies the effect of these . perturbations. In the so-called direct method one characterises the solution in a way with respect to stability which is not necessarily local.
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