Displaying similar documents to “On the phase portrait of the fast filtering algorithms”

Dispersions for linear differential equations of arbitrary order

František Neuman (1997)

Archivum Mathematicum

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For linear differential equations of the second order in the Jacobi form y ' ' + p ( x ) y = 0 O. Borvka introduced a notion of dispersion. Here we generalize this notion to certain classes of linear differential equations of arbitrary order. Connection with Abel’s functional equation is derived. Relations between asymptotic behaviour of solutions of these equations and distribution of zeros of their solutions are also investigated.

The nonlinearly damped oscillator

Juan Luis Vázquez (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the large-time behaviour of the nonlinear oscillator m x ' ' + f ( x ' ) + k x = 0 , where m , k > 0 and f is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case f ( x ' ) = A | x ' | α - 1 x ' with α real, A > 0 . We characterize the existence and behaviour of fast orbits, i.e., orbits that stop in finite time.