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Abstract: 

We study the properties of a system stochastic differential equations to elucidate the effect that uncertainty can play in non-linear dynamical systems.  The specific example is the stochastic Gause predator-prey model.  These equations model the dynamics of a system where the predation rate is given by a functional response of the prey, and the prey obeys logistic growth. The noise models the uncertainty in the equation’s parameters and is included as an additive but non-linear Gaussian process.  We show conditions for existence and boundedness of the solutions for different types of Holling functional response models.  We also show the possibility of noise-induced extinction events in situations where the deterministic dynamics allow for coexistence.  Finally, we give conditions on the noise and model parameters for the existence of an invariant distribution.

Speaker’s Bio: 

Jorge is an applied mathematician, educator, and researcher.  He was born and raised in Medellín, Colombia, where he attended engineering school.  Later he obtained a Ph.D. in mathematics at Oregon State University and held a postdoctoral position in the mathematics department at the University of Arizona.  From 2009 until 2021, Jorge worked as an associate professor in mathematics in his hometown, at the Universidad Nacional de Colombia.  He joined the Systems and Decision Sciences group at the Oak Ridge National Laboratory in February of 2022 where he conducts interdisciplinary research in the theory, modeling, and computation of stochastic processes applied to the natural and life sciences.