Emergence of complex structure in a model of evolving networks

Professor Sanjay Jain, Indian Institute of Science and Santa Fe Institute

A mathematical model of dynamical networks motivated by prebiotic chemical evolution will be described. The network spontaneously becomes more complex and structured via a self-organization process triggered by the chance, but inevitable, appearance of autocatalytic sets. Over long time scales the network exhibits complex dynamics including crashes caused by the elimination of keystone nodes, followed by recoveries due to the re-emergence of autocatalytic sets. This fragility of the otherwise robust autocatalytic structure can be traced to a slow internal reorganization of the network caused by the evolution rule. Analytically determined time scales for the self-organization processes which depend upon system parameters via power laws, as well as quantitive measures of network complexity and structure will be discussed.