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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Discretization and Implicit Mapping Dynamics (Hardcover, 1st ed. 2015)
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Discretization and Implicit Mapping Dynamics (Hardcover, 1st ed. 2015)
Series: Nonlinear Physical Science
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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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