[PDF] Periodic Solutions Of Nonlinear Dynamical Systems eBook

Author : Eduard Reithmeier
Publisher : Springer
Page : 177 pages
File Size : 36,52 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540384278

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Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly from the field of nonlinear vibrations. The text addresses mathematicians interested in engineering problems as well as engineers working with nonlinear dynamics.

Author : Albert C.J. Luo
Publisher : Springer
Page : 210 pages
File Size : 13,38 MB
Release : 2016-01-28
Category : Technology & Engineering
ISBN : 3319266306

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The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 47,60 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642971490

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Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.

Author : Dominic William Jordan
Publisher : Oxford University Press, USA
Page : 564 pages
File Size : 45,44 MB
Release : 1999
Category : Mathematics
ISBN : 9780198565628

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This edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos.

Author : E. Atlee Jackson
Publisher : CUP Archive
Page : 676 pages
File Size : 45,89 MB
Release : 1989
Category : Mathematics
ISBN : 9780521426336

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The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations.

Author : Vasile Marinca
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 12,42 MB
Release : 2012-01-05
Category : Technology & Engineering
ISBN : 3642227341

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This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.

Author : H.G Solari
Publisher : Routledge
Page : 369 pages
File Size : 26,99 MB
Release : 2019-01-22
Category : Mathematics
ISBN : 1351428306

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Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and work

Author : E. Atlee Jackson
Publisher : CUP Archive
Page : 532 pages
File Size : 10,56 MB
Release : 1989
Category : Mathematics
ISBN : 9780521426329

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The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.