arXiv subjects

Andrew Vlasic

Publications and source records attributed to Andrew Vlasic.

21 records · Page 2Linked to original sources

arXiv2014

Long-Run Analysis of the Stochastic Replicator Dynamics in the Presence of Random Jumps

A further generalization of the stochastic replicator dynamic derived by Fudenberg and Harris \cite{FH92} is considered. In particular, a Poissonian integral is introduced to the fitness to simulate the affects of anomalous events. For the two strategy population, an estimation of the long run behavior of the dynamic is derived. For the population with many strategies, conditions for stability to pure strict Nash equilibria, extinction of dominated pure strategies, and recurrence in a neighborhood of an internal evolutionary stable strategy are derived. This extends the results given by Imhof \cite{I05}.

q-bio.PE↗

arXiv2013

Mean Evolutionary Dynamics for Stochastically Switching Environments

Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models including the replicator dynamic for linear symmetric and asymmetric landscapes, the Moran process, and incentive dynamics. We give a simple relationship between the probability of environmental switching, the relative fitness gain, and the effect on long term behavior in terms of fixation probabilities and long term outcomes for deterministic dynamics. We also discuss cases where the dynamic changes, for instance a population evolving under a replicator dynamic switching to a best-reply dynamic and vice-versa, giving Lyapunov stability results.

math.DS↗

arXiv2012

Modeling Stochastic Anomalies in an SIS and SIRS System

I propose a stochastic SIS and SIRS system to include a Poisson measure term to model anomalies in the dynamics. In particular the positive integrand in the Poisson term is intended to model quarantine. Conditions are given for the stability of the disease free equilibrium for both systems.

math.PR↗