Analysis of complexity in a competitive-cooperative-mixed multiagent system

LEONIDAS F. CARAM; MARCEL AUSLOOS; NAHUEL ALMEIRA; CESAR F. CAIAFA

Santiago

Conferencia; XX Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics - MEDYFINOL 2018; 2018

Universidad de los Andes

In this work, we consider a network system with competition and collaboration between different sets of agents following a generalized Lotka-Volterra model. This model was already proposed and its dynamics analysed in its purely competitive [1] and collaborative [2] versions. Recently, a mixed interaction scheme among three agents was proposed and analyzed in [3]. Motivated by our previous results [4], here we consider a network with 10 agents whose ?adjacency? matrix of interactions is symmetric and chosen at random keeping an even ratio of competitive and collaborative interactions. In other words, we considered an adjacency matrix having half of agents collaborating and the other half competing. We provide a simulation based analysis by generating time series of 10 interacting agents using a fixed initial condition in all cases and a randomly generated adjacency matrix in each simulation. Then, we applied a Bandt and Pompe analysis (ordinal patterns) [5] to find out the pattern distributions, determine the Shannon Entropy (H) associated with it, compute the Disequilibrium (D) (Euclidean distance) [6,7] and, finally, obtain the statistical complexity (C) of the system, i.e. C=DH.We found that, by changing only the structure of network interactions, the system can show very different dynamics, from converging to a stable fixed point up to showing chaotic behavior. More interestingly, by analyzing the histogram of the time series complexities, two distinct groups are clearly identified: (I) a high complexity group with low dispersion and (II) a low complexity group with a higher dispersion.