Discrete Dynamics in Nature and Society
Volume 2 (1998), Issue 3, Pages 167-172

Dynamic ensembles with variable structure and friction simulation

I. V. Feldstein and N. N. Kuzmin

Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, Russia

Received 1 February 1998

Copyright © 1998 I. V. Feldstein and N. N. Kuzmin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper presents an approach to the simulation of friction interaction. The model does not use any physical descriptions of the processes in the system, but it has simple physical interpretation. It is based on one qualitative experimental result – the value of first Lyapunov exponent drops with normal load. It is shown that the logistic map could be considered as the simplest model of continuous contact. The generalization of the model (which takes into account the discreteness of the real contact) gives results very similar to the experimental ones. It is in the form of a dynamic ensemble with variable structure (DEVS), which has some interesting properties – particularly bifurcation diagrams.