complex systems update

scientific

complex systems are composed of many interconnected parts and cannot be tackled analytically, i.e., by using closed-form mathematical expressions. complex systems come from many domains:

• socio-economic
  
• technological
  
• biological

Complex systems are often represented by networks; source.

they are typically characterized by non-linear behavior, display emergence ("the whole is greater than the sum of its parts") and are highly adaptive.

complex systems can be viewed as the current frontier in the understanding of the workings of nature, which started with the analysis of liner systems described by few variables:

(source: s. strogatz; "nonlinear dynamics and chaos"; 2001)

there are arguably two main strands in the study of complex systems:

1. complexity science or complex adaptive systems
   
2. multi-agent systems
   

the former fields find their moder incarnation mostly in the form of complex network theory, where the system's elements are represented by nodes in a graph, and their interactions are defined by the graphs edges. complex networks can have three levels of description:

1. direction of links
2. weights of links
3. variables assigned to nodes

the topology of the network often reflects its function.

multi-agent systems originate from the computational approach of agent-based modeling. agents interact with each other through local rules. often the evolution of these systems can only be known by letting the actual simulation evolve.


(source: wikipedia, complexity map overview)

slowly however, the focus has shifted on merging the two strands. in may 2010 there will be a workshop on "emergent intelligence on networked agents". from the description:

the intention of this workshop is to [bridge] the gap between the two research communities in complex networks and multi-agent systems.

currently, it seems that research on multi-agent systems is still mostly focused on agents themselves, whereas networks of agents have received relatively little attention.

a framework to model these multi-agent systems is provided by the complex networks approach [...]. thus, the underlying network structure of a multi-agent system plays a crucial role in explaining emergent properties. networked agents, on the other hand, may be able to actively change this structure by forming new links or cutting existing ones. consequently, there is not only a strong relation, but a coevolution in the dynamics of agents and their network of interactions.