Published: 31 December 2008

Paradoxes of increasing linear damping in the nonlinear driven oscillators

R. S. Smirnova1
M. V. Zakrzhevsky2
V. Yu. Yevstignejev3
I. T. Schukin4
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The work is devoted to the systematic study of periodic and chaotic forced oscillations. Recently, on the basis of method of complete bifurcation groups new nonlinear effects were found in driven damped systems with various nonlinearities of elastic restoring forces. Construction of complete bifurcation groups is based on the method of stable and unstable periodic regimes continuation on parameter. Aim of the work – to study new nonlinear effects induced by varying linear dissipation in following dynamical systems with typical nonlinear restoring forces: symmetric trilinear and quadratic, bilinear, cubic with asymmetry, Duffing, pendulum. The work presents new qualitative and quantitative results of nonlinear dynamics in the systems with increasing linear dissipation

About this article

20 September 2008
02 December 2008
31 December 2008
forced nonlinear oscillations
linear damping
unstable periodic infinitiums
rare attractors
chaotic attractors
complete bifurcation analysis