# Dynamic Peer-to-Peer Competition - Nonlinear Sciences > Chaotic Dynamics

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Abstract: The dynamic behavior of a multiagent system in which the agent size $s {i}$is variable it is studied along a Lotka-Volterra approach. The agent size hashereby for meaning the fraction of a given market that an agent is able tocapture market share. A Lotka-Volterra system of equations for prey-predatorproblems is considered, the competition factor being related to the differencein size between the agents in a one-on-one competition. This mechanismintroduces a natural self-organized dynamic competition among agents. In thecompetition factor, a parameter $\sigma$ is introduced for scaling theintensity of agent size similarity, which varies in each iteration cycle. Thefixed points of this system are analytically found and their stability analyzedfor small systems with $n=5$ agents. We have found that different scenariosare possible, from chaotic to non-chaotic motion with cluster formation asfunction of the $\sigma$ parameter and depending on the initial conditionsimposed to the system. The present contribution aim is to show how a realisticthough minimalist nonlinear dynamics model can be used to describe marketcompetition companies, brokers, decision makers among other opinion makercommunities.

Autor: L. F. Caram, C. F. Caiafa, A. N. Proto, M. Ausloos

Fuente: https://arxiv.org/