EAN: 9783662472743

DISCRETIZATION AND IMPLICIT MAPPING DYNAMICS - ...

This unique book presents the discretization of continuous systems and implicit mapping
dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and
bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed  and the
explicit and implicit maps of continuous dynamical systems are developed through the
single-step and multi-step discretizations. The implicit dynamics of period-m solutions in
discrete nonlinear systems are discussed. The book also offers a generalized approach to
finding analytical and numerical solutions of stable and unstable periodic flows to chaos in
nonlinear systems with without time-delay. The bifurcation trees of periodic motions to chaos
in the Duffing oscillator are shown as a sample problem  while the discrete Fourier series of
periodic motions and chaos are also presented. The book offers a valuable resource for
university students  professors  researchers and engineers in the fields of applied mathematics
physics  mechanics  control systems  and engineering.

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