Complex adaptive systems

Abstract

Examples for complex adaptive systems (CAS) are the brain, whose neurons are connected by synapses to a complex network, the network of chemical reactions in prebiotic evolution, the control network of our immune system, and social or economical networks whose dynamics could be described as an evolutionary game. All of these systems have a common structure: They consist of a network of elements (e.g. neurons, genes, agents in a game,...), interacting nonlinearly with themselves and with their environment. They receive information from their environment (that could also consist of other species), and transform this knowledge into actions yielding certain advantages (reward, more descendants). These transformations, using also information from memory, are in fact a very general form of a computation. The main element which distinguishes complex adaptive systems from pure logical machines is their ability to adapt or to change their computations and programs in dependence of the reward, where the goal is to achieve an optimal advantage. In other words, the systems considered are adaptive, while the respective systems determining the reward associate a meaning to the computation, a fact which is missing when pure logic machines are concerned. Being coupled nonlinear systems, their behaviour can be described using methods of nonlinear dynamics. My lectures at the Heraeus Seminar in Chemnitz were mostly based on sections of my new introductory book: Complex Adaptive Systems [1]. In the following we discuss the behavior of two complex adaptive systems which were also presented in the lectures but which are not described in this book. The first example provides the arguably simplest model of a system that can learn something about itself. We will show how a system can find its status in a hierarchy of agents by using the reflexes of other agents as a mirror. The second example is the so called minority game. There we will show how a group of adaptive agents can predict the optimal occupancy of a restaurant or the least crowded, but still promising stock on a market. © Springer-Verlag Berlin Heidelberg 2005.