CICLO DE SEMINARIOS EN BIOMATEMÁTICA - IDEUV 2022, Modalidad Virtual

Plataforma Zoom (ID: 829 1194 9484    PASSCODE: 285888)

28, Julio 2022


"Some limit results of a system of interacting stochastic replicators."
Resumen: "In this work we build a system of interacting stochastic replicators from which we analyze some limit behaviors. On the one hand, a spatial limit, where we study the convergence of the system (in some adequate sense) when the number of replicators grows to infinity; and on the other hand, a time limit, in which we give conditions for the existence of a single non-trivial invariant measure. The result of the spatial limit leads us to a Mckean-Vlasov type system on the simplex via a propagation of chaos' result, where such a limit system will represent the behavior of an "ideal replicator" in an environment composed by an infinity of them that interact through their energy diffusions. On the other hand, both in the system composed of N interacting replicators and in the ideal limit, similar conditions can be established for the existence of a unique invariant measure in the interior of the N-simplex and the simplex, respectively, providing these systems with the Strong Stochastic Persistence (SSP) property."
 
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