Emergent Structures in Dissipative Wave-Particle Systems

We study the motion of a particle with mass m on a vibrated string of length L. We assume that there is a friction force between the particle and the string. The string is sinusoidally forced at both ends. We find that the particle has attractors located at x=L/2 - $n\pi c/2 \omega$, where $\omega$ is the frequency of the waves on the string, and $n \in {\boldmath Z}$. We also study the attractors of the same system with multiple driving frequencies. We also compared our results with numerical simulations.