A general classification of the replication dynamics with a unique fixed point in the interior of simplex
Organizations: School of Mathematics and Statistics, Guilin University of Technology, Guilin, Guangxi, China · Guangxi Colleges and Universities Key Laboratory of Applied Statistics, Guilin, Guangxi, China · Computational Biology and Medical Ecology Lab Biostatistics and Image Genetics Lab Kunming Institute of Zoology, Chinese Academy of Sciences, Kunming, China · Kunming College of Life Sciences, University of Chinese Academy of Sciences, Kunming, China · Faculty of Arts and Sciences Harvard University Cambridge, MA, 02138, USA
Abstract
The replication dynamics (differential equation system) is the foundation of evolutionary game theory. When n=2, there are four possible types of replication dynamics. When n=3, there are 49 possible types of replication dynamics. However, when n>3, the classification of replication dynamics has not been solved. In this article, the sufficient and necessary conditions of the replication dynamics equation with a unique fixed point in the interior of simplex (Int) for are presented. Furthermore, the different types of replication dynamics equations with a unique fixed point in IntSn is discussed.