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Proceedings Paper

Feedback coupling in dynamical systems
Author(s): Steffen Trimper; Knud Zabrocki
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Paper Abstract

Different evolution models are considered with feedback-couplings. In particular, we study the Lotka-Volterra system under the influence of a cumulative term, the Ginzburg-Landau model with a convolution memory term and chemical rate equations with time delay. The memory leads to a modified dynamical behavior. In case of a positive coupling the generalized Lotka-Volterra system exhibits a maximum gain achieved after a finite time, but the population will die out in the long time limit. In the opposite case, the time evolution is terminated in a crash. Due to the nonlinear feedback coupling the two branches of a bistable model are controlled by the the strength and the sign of the memory. For a negative coupling the system is able to switch over between both branches of the stationary solution. The dynamics of the system is further controlled by the initial condition. The diffusion-limited reaction is likewise studied in case the reacting entities are not available simultaneously. Whereas for an external feedback the dynamics is altered, but the stationary solution remain unchanged, a self-organized internal feedback leads to a time persistent solution.

Paper Details

Date Published: 7 May 2003
PDF: 10 pages
Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); doi: 10.1117/12.488997
Show Author Affiliations
Steffen Trimper, Martin-Luther-Univ. Halle-Wittenberg (Germany)
Knud Zabrocki, Martin-Luther-Univ. Halle-Wittenberg (Germany)

Published in SPIE Proceedings Vol. 5114:
Noise in Complex Systems and Stochastic Dynamics
Lutz Schimansky-Geier; Derek Abbott; Alexander Neiman; Christian Van den Broeck, Editor(s)

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