Dynamics of competence and cooperation in a 2D-lattice with neighbour structure

CESAR F. CAIAFA; ARACELI N. PROTO

Santiago de Chile, CHILE

Congreso; International Congress on the Applications of Mathematics - ICAM 2006; 2006

Universidad de Chile

In this paper, we study the dynamical properties of a nonlinear system defined by a generalization of the LotkaVolterra equations for a 2Dlattice where interactions among agents are restricted to have a nearest neighbor spatial structure. As we show in this work, the model leads to interesting dynamical properties, the fixed points are theoretically determined and the stability analysis is provided. The present model is able to describe cooperation as well as competence among neighbors through an interaction parameter gamma. It is showed that, for a moderate level of interaction (|gamma|< alpha/4) all agents tend to adopt an uniform value, but, when the competence is agressive (|gamma|> alpha/4), then agents tend to adopt a polarized configuration called the "chessboard" configuration. Some computer simulation results are shown giving a validation of our theoretical results.