Evolving Networks with Desired Dynamics
Abstract
Networks giving rise to complex dynamics exist in a wide range of physical, biological and engineered systems. Recent studies have focused on the structure of such networks, and examined how the structure is linked to functional properties such as robustness and error tolerance. In general, however, a theory to predict the dynamics based on the network structure is lacking, and consequently, it is often unclear what structural architecture is needed to produce desired dynamics. Here we show that networks with desired complex dynamics can be obtained by evolving their structure rather than by designing it from the outset. We study a class of differential equations that have been proposed as a mathematical model of genetic networks, and construct and experimentally analyze an electronic circuit that displays the same dynamics as the differential equations. These networks can display a variety of behaviors, including fixed points, limit cycles and chaos. Here we focus on limit cycles and show that it is possible to evolve networks that display stable oscillations of a specified cycle length. We also demonstrate that there is an optimal evolution rate for obtaining such dynamics. This work offers novel insights into how mutations can alter network dynamics.
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 2004
- Bibcode:
- 2004APS..MARV18009M