War: Origins and Effects
  The International System is a self-organized system that shows emergent behavior. During the timeframe (1495-1945) covered in this study, a finite-time singularity and four accompanying accelerating log-periodic cycles shaped the dynamics of the International System. Each cycle began and ended with a systemic war. During their life span, these cycles show remarkable regularities in their dynamics. The accelerated growth of the connectivity of the regulatory network of the International System, in combination with its anarchistic structure, produce and shape the war dynamics of the system. The accelerated growth of the connectivity of the International System is fed by population growth and the need for social systems to fulfill basic requirements. The finite-time singularity and accompanying log-periodic oscillations were instrumental in the periodic reorganization of the regulatory network of the International System and contributed to a long-term process of social expansion and integration in Europe. The singularity dynamic produced a series of organizational innovations. At the critical time of the singularity (1939), the connectivity of the system reached a critical threshold and resulted in a critical transition that led to a fundamental reorganization of the International System. Europe transformed from an anarchistic system to a cooperative security community. During the life span of the cycles, the war dynamics showed chaotic characteristics. These findings have implications for the social sciences and historical research. 
Ingo Piepers
physics.soc-ph nlin.AO