Attractor's capture probability in nonlinear argumental oscillators
Résumé
The behavior of a space-modulated, so-called 'argumental' Duffing oscillator, is studied. Starting from a known analytic implicit solution to the equations of motion, and using a Van der Pol representation in the (amplitude, phase)-space, the shape and distribution of the attractors' upstream basins are discussed, and various capture probabilities by the at- tractors are assessed under symbolic form. The expressions obtained can help in the design of structures in mechanical engineering, where most often the argumental phenomenon is to be avoided.