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Periodic Solutions of Nonlinear Dynamical Systems - Numerical Computation, Stability, Bifurcation and Transition to Chaos (Paperback, 1991 ed.)
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Periodic Solutions of Nonlinear Dynamical Systems - Numerical Computation, Stability, Bifurcation and Transition to Chaos (Paperback, 1991 ed.)
Series: Lecture Notes in Mathematics, 1483
Expected to ship within 10 - 15 working days
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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.
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