13 citations · 45 across the 7 of their papers we have counts for
7 papers
Asymmetric Duffing oscillator: jump manifold and border set
Jan Kyzioł, Andrzej Okniński
We study the jump phenomenon present in the forced asymmetric Duffing oscillator using the known steady-state asymptotic solution. The major result is the computation of the jump m…
Duffing-type equations: singular points of amplitude profiles and bifurcations
Jan Kyzioł, Andrzej Okniński
We study the Duffing equation and its generalizations with polynomial nonlinearities. Recently, we have demonstrated that metamorphoses of the amplitude response curves, computed b…
Effective equation for two coupled oscillators: towards a global view of metamorphoses of the amplitude profiles
Jan Kyzioł, Andrzej Okniński
Dynamics of nonlinear coupled driven oscillators is investigated. Recently, we have demonstrated that the amplitude profiles -- dependence of the amplitude on frequency of…
Van der Pol - Duffing oscillator: global view of metamorphoses of the amplitude profiles
Jan Kyzioł, Andrzej Okniński
Dynamics of the Duffing--Van der Pol driven oscillator is investigated. Periodic steady-state solutions of the corresponding equation are computed within the Krylov-Bogoliubov-Mitr…
Exact nonlinear fourth-order equation for two coupled nonlinear oscillators: metamorphoses of resonance curves
Jan Kyziol, Andrzej Okninski
We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear fourth-order equation describing inner dynamics.…
Coupled nonlinear oscillators: metamorphoses of amplitude profiles for the approximate effective equation - the case of 1:3 resonance
Jan Kyziol, Andrzej Okninski
We study dynamics of two coupled periodically driven oscillators. An important example of such a system is a dynamic vibration absorber which consists of a small mass attached to t…
Coupled nonlinear oscillators: metamorphoses of amplitude profiles. The case of the approximate effective equation
Jan Kyziol, Andrzej Okninski
We study dynamics of two coupled periodically driven oscillators. Important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the…