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標(biāo)題: Titlebook: Bifurcation and Chaos in Engineering; Yushu Chen,Andrew Y. T. Leung Book 1998 Springer-Verlag London Limited 1998 Vibration.algorithms.cal [打印本頁]

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Book 1998ural engineering), the discovery of irregular vibrations in addition to periodic and almost periodic vibrations is one of the most significant achievements of modern science. An in-depth study of the theory and application of non-linear science will certainly change one‘s perception of numerous non-
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https://doi.org/10.1007/978-981-10-1011-8mical behaviour of the semi-infinite time domain. The theory of the averaging method has various forms. When we describe the averaging method in the theory of bifurcation, we base our statements on the work of KBM and Hale (J.K. Hale) [30].
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https://doi.org/10.1007/978-1-4471-1575-5Vibration; algorithms; calculus; chaos; design; differential equation; dynamical systems; engineering desig
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978-1-4471-1577-9Springer-Verlag London Limited 1998
作者: 乏味    時間: 2025-3-24 05:29
VOM PROBLEMBEZIRK ZUM KUNSTQUARTIER,In this chapter, section 5.1 studies another main method for the local bifurcation of dynamical systems: the Centre Manifold Theorem. In section 5.2, the centre manifold theorem is used to analyse simple bifurcation. In the section 5.3, the Normal Form theory of vector fields is introduced.
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Sharon Vaughn,Ruth McIntosh,Anne HoganWe include three computational methods in this chapter, namely normal form theory, symplectic integration and the imbedded partial differential equation method.
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Hopf Bifurcation,Periodic vibration phenomena can be found in many non-conservative systems in nature. Hopf bifurcation theory is a theory that studies the modern development of period vibration phenomena. In this chapter we introduce the method of studying the Hopf bifurcation of autonomous systems by the normal form theory.
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Interpret the Results (Worksheet F)ng properties of discrete systems. Because research on discrete dynamical systems is relatively simple and straightforward, theorems on diffeomorphism are often presented first, followed by the relevant discussion. In addition, flows are sometimes discretized in order to obtain their properties by s
作者: 被告    時間: 2025-3-26 11:57
Define the Outcome (Worksheet D)inary differential equations, Liapunov—Schmidt reduction (LS reduction for short), singularity theory and applications of all these theories. Chapter 5 introduces the centre manifold theorem and the normal form of vector fields. Chapter 6 presents the Hopf bifurcation and double zero eigenvalues. Ch
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https://doi.org/10.1007/978-981-10-1011-8, algebraically iterative equations, etc.) chaos has attracted wide attention. So far no strict general mathematical definition of chaos has been available, but it is depicted in many different ways. It is found in a wide variety of fields, such as mathematics, physics, mechanics, astronomy, chemica
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Candace S. Bos,Patricia L. Anderscs of the solutions, such as the number of solutions, the type and periodicity of the solutions and, more importantly, the existence of chaotic solutions, are of great interest in a physical parametric space. The boundaries separating qualitatively different solutions in a physical parametric space,
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Dynamical Systems, Ordinary Differential Equations and Stability of Motion, important properties by means of examples. Sections 1.4 and 1.6 discuss the important properties of the limit set in plane, especially the Poincaré-Bendixson theorem and its application. Also touched on are the basic concepts of initial value problems in ordinary differential equations and the basic concepts of Liapunov’s stability of motion.
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Calculation of Flows, with the algebric characteristics and calculations of linear flows in section 2.2. Section 2.3 discusses linearly hyperbolic flows and their classification. Section 2.4 deals with calculations of local flows of non-linear system. Finally, we introduce the stable manifold theorem.
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Non-Linear Structural Dynamics, to explain the generality and importance of non-linear dynamic problems, we introduce some engineering examples of bifurcation theory. The examples include the buckling of a bar, the flutter of an elastic structure, the non-linear resonance of an unbalanced rotating shaft with internal damping, gal
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Construction of Chaotic Regions, differential equations arise from various types of physical and engineering problems. Owing to the presence of non-linearities, analytical solutions are rarely obtained. Apart from their deterministic nature, random-like solutions are observed for certain parameters and initial conditions. The occu




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