Modeling the Limit-cycle Behavior of Technoeconomic Systems

Organized by the Complex Systems Modeling Research Focus Area of the Modeling, Algorithms, and Informatics Group (CCS-3).

Tessaleno Devezas, Universidade da Beira Interior, Portugal.

April 24, MST-8 Auditorium, TA 3, building 1698, room A103, 2:00-3:30pm.

May 1, MST-8 Auditorium, TA 3, building 1698, room A103, 3:00-4:30pm.

In a series of two talks we will present the main concepts and ideas developed in four recent papers, two of them already published and two in preparation:


The technoeconomic system is an evolving complex adaptive system with many kinds of participants, which interact in intricate ways that continually reshape their collective future. During the ongoing evolutionary process the system self-organizes and learns to configure and reconfigure itself towards greater efficiency in the midst of greater complexity. Each stage of the evolutionary process corresponds to a given structure that encompasses previous self-organization, learning and current limitations. This is to say that self-organization and learning are embodied in the system’s structure and the collective learning rate is an overall system’s property. Such stages of the evolutionary path of a technoconomic system are well described by simple logistic curves that to some extent conceal the complexity of mechanisms involved.
In the above papers a cybernetic framework is proposed which, using a chaos based approach, may help to unveil some hidden properties of the logistic learning collective dynamics. From the relationship between the differential and the discrete logistic equations, it is demonstrated that the unfolding of a logistic (learning) process is constrained by two control parameters: the aggregate learning rate d and a generation-related characteristic time tG, whose product is maintained in the interval 3 < δ. tG < 4 (deterministic chaos) grants the enduring evolutionary process. Describing the technoeconomic system discretely as a logistic growing number of “interactors” adopting a new set of ideas (“new learning”), and using the logistic function as the probabilistic distribution of individuals exchanging and processing information in a finite niche of available information, it is demonstrated that the rate of information entropy change (K-entropy) exhibits a four-phased limit-cycle behavior. Moreover it is speculated that social systems mimic living systems as efficient negentropic machines, and making use of Prigogine’s entropy balance equation for open systems it is suggested that its cyclical behavior is probably the best way to follow nature’s efficiency strategy.
This model corroborates previous abundant empirical data on the duration and general features of long waves in economics (K-waves) and was very recently successfully applied to describe the unfolding and growth of the Internet. Implications of this modeling on reducing logical uncertainties in predicting the behavior of social systems, and the possibility of its use as a most general evolutionary algorithm for describing co-evolutionary social processes will be discussed.

For more information contact Luis Rocha at
Last Modified: April 18, 2002