title: Evolution kinetics and phase transitions of complex adaptive systems.
abstract: Motivated by the fact that a population of competing agents never set up a true stationary distribution, we propose a theory of evolution kinetics for complex adaptive systems. The formula derived for the survival probability is used to describe different phases in the population evolution when the prize-to-fine ratio as well as time changes. A kinetic phase diagram is obtained to show the phase boundaries for the self-segregating region, the intermediate region, and the clustering region. The kinetic evolutionary equations of strategy distribution are also established and used to give the root-mean-square separation of strategy distribution. It is revealed that the rootstock of the phase transitions is ascribed to the cooperation and competition among agents with different gene values for a limited resource.
authors.affiliation: National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China.
authors.forename: Bing-Zhen
authors.initials: BZ
authors.lastname: Xu
authors.forename: Guojun
authors.initials: G
authors.lastname: Jin
authors.forename: Yuqiang
authors.initials: Y
authors.lastname: Ma
mesh_terms: D000222:Adaptation, Physiological / Q000502:physiology*; D000818:Animals; D005075:Biological Evolution; D003163:Competitive Behavior; D003198:Computer Simulation; D017753:Ecosystem; D005716:Game Theory; D006801:Humans; D007700:Kinetics; D008954:Models, Biological; D015233:Models, Statistical; D044367:Phase Transition; D011157:Population Dynamics; D011158:Population Growth; D012641:Selection, Genetic; D016019:Survival Analysis; D015996:Survival Rate