Diversity, mobility and cyclic competition in social and ecological systems

Abstract

The interest of physicists in interdisciplinary problems has increased in the last few years, with the study of complex systems. Tools from statistical mechanics, dynamic systems and other traditional areas have been applied to sociology, economy and biology problems, among others. In this project, we propose to study models defined in networks, that have the property of locally inhibit diversity (homogenizing the states of the agents) and investigate in which conditions such models would be able to sustain global diversity (preventing the homogenization from spreading to the whole network). This problem has applications in sociology, as it would explain the persistence of differing points of view in societies, and also in biology, where it can explain biodiversity. We intend to use generalizations of the Sznajd model (with the inclusion of confidence rules), of the voter model and models based in game theory. Particularly, we would like to study the role of the network topology, paying special attention to the small world property, as well as the role played by cyclic competition, in order for diversity to be sustained in these models. We intend to use in our study, computer simulations, complemented by analytic tools. (AU)