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

N. ALMEIRA; M. AUSLOOS; L.F. CARAM; C.F. CAIAFA

Santiago

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

Universidad de los Andes, Santiago de Chile

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 matrix of interactions is symmetric and chosen at random keeping an even ratio of competitive and collaborative interactions. In other words, the matrix of interactions contains 50% of positive values leaving the other 50% filled with negative values.We provide a simulation based analysis by generating time series of 10 interacting agents using a fixed initial condition in all the cases and randomly generated iterations. Then, we apply 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) [6,7] and, finally, obtain the statistical complexity 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 to a chaotic behavior. More interestingly, by analyzing the histogram of the time series complexities, two distinctive groups are clearly identified: (I)high complexity group and (II) low complexity group with mean values around 0.11 and 0.04, respectively. In the future, we plan to investigate how the structure of network interactions is related to a low or high complexity as observed in the time series.[1] L. Caram, C. Caiafa, A. Proto, M. Ausloos, Physica A: Statistical Mechanics and its Applications 389, 2628 (2010).[2] LF. Caram, CF. Caiafa, AN. Proto, M. Ausloos, Physical Review E 92(2), 022805 (2015).[3] PT. Simin, GR. Jafari, M. Ausloos, CF Caiafa, LF. Caram, A. Sonubi, A. Arcagni, S. Stefani, The European Physical Journal B 91(43) (2018).[4] LF. Caram, M. Ausloos, CF. Caiafa, LANET 2017 Proceedings, Puebla, Mexico (2017).[5] C. Bandt and B. Pompe, Physical review letters, 88 (17) (2002).[6] X. Calbet, R. Lopez-Ruiz, Physical Review E 63(6), 066116 (2001).[7] OA. Rosso, MT. Martín, HA. Larrondo, AM. Kowalski and A. Plastino, Concepts and Recent Advances in Generalized Information Measures and Statistics Ch 8 (2013).