Evolution of cooperation and population dynamics using cellular automata and complex networks

• Grant number: 15/01032-9
• Support Opportunities: Regular Research Grants
• Duration: June 01, 2015 - May 31, 2017
• Field of knowledge: Interdisciplinary Subjects
• Principal Investigator: Pedro Henrique Triguis Schimit
• Grantee: Pedro Henrique Triguis Schimit
• Host Institution: Universidade Nove de Julho (UNINOVE). Campus Memorial. São Paulo , SP, Brazil
• Associated researchers: Fabio Henrique Pereira

Abstract

We propose mathematical models where population dynamics can be simulated, in an attempt to understand its rules, define parameters and predict its behavior. Population will be simulated using cellular automata, where neighborhood rules will also be considered a complex network formed by individuals. Their interactions will be explored according to a benefit competition, modeled by game theory, where each interaction is a game that gives each individual a payoff. Therefore, it will be possible to stress either how the network influences the evolution of cooperation, or if a very connected population is more susceptible to cooperation. Here, the problems will be considered: disease spreading; benefit competition and how it may lead to a cooperation scenario; ordinary differential equation for those models; and analysis of previous data with topological parameters from individuals' network.In the topic of disease spreading, after modeling the population in cellular automata, ordinary differential equation, and complex network, we will analyze how the individuals' rational behavior influences the vaccination level in population. The point is: If all individuals play rationally, will the population decimate the disease?Evolution of cooperation is hard to understand, since in some daily situations is better to cheat than cooperate, so why do we cooperate? We also use cellular automata, ordinary differential equation and complex networks in order to understand what influences the cooperation level in a population. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SCHIMIT, P. H. T.. Evolutionary aspects of spatial Prisoner's Dilemma in a population modeled by continuous probabilistic cellular automata and genetic algorithm.. Applied Mathematics and Computation, v. 290, p. 178-188, NOV 1 2016. (15/01032-9)

SCHIMIT, P. H. T.; BARROS JUNIOR, D. F.; ARAUJO, S. A.. On estimating the impact of information spreading in a consumer market modeled by probabilistic cellular automata and ordinary differential equations. SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION INTERNATIONAL, v. 93, n. 12, p. 1063-1072, DEC 2017. (15/01032-9)

SCHIMIT, P. H. T.; SANTOS, B. O.; SOARES, C. A.. Evolution of cooperation in Axelrod tournament using cellular automata. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 437, p. 204-217, NOV 1 2015. (15/01032-9)