Periodic Solutions of Nonlinear Dynamical Systems

Numerical Computation, Stability, Bifurcation and Transition to Chaos

Eduard Reithmeier (Autor)

Buch | Softcover

VI, 174 Seiten

1991 | 1991
Springer Berlin (Verlag)
978-3-540-54512-5 (ISBN)

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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.

Differentiable dynamical systems.- Differentiable dynamical systems with discontinuities.

Erscheint lt. Verlag	25.9.1991
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VI, 174 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	281 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
Schlagworte	algorithm • algorithms • Chaos • Dynamical system • Dynamical Systems • Dynamische Systeme • Nonlinear Dynamics • Vibration
ISBN-10	3-540-54512-3 / 3540545123
ISBN-13	978-3-540-54512-5 / 9783540545125
Zustand	Neuware