Discrete Dynamics in Nature and Society
Volume 1 (1997), Issue 2, Pages 127-134

Active stabilization of a chaotic urban system

Günter Haag, Tilo Hagel, and Timm Sigg

Institute of Theoretical Physics, University of Stuttgart, Pfaffenwaldring 57/III, Stuttgart D-70550, Germany

Received 9 October 1996

Copyright © 1997 Günter Haag et al. 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.


A new method to stabilize dynamical systems by forcing the system variables into the desired unstable stationary point is proposed. The key conception of the method is based on parametric perturbation. This means that the equations of motion are influenced by continuous variation of some selected parameters. Thus – without using any external forces – the motion of the system approaches the chosen unstable stationary point. The variation of the parameters will vanish after the successful stabilization. Therefore, the system and its parameters are changed during the control process only. The algorithm is applied to an urban system within a metropolitan area obeying a Lorenz-type dynamics as well as to the Hénon attractor as an example for a discrete scenario.