Abstract

Evolutionary Computation refers to a broad family of population-based heuristic approaches within the field of Artificial Intelligence that are inspired by natural evolution. This talk will focus on coevolutionary systems, which involved a large population of adaptive agents whose behavioral changes are guided only by their interactions. In particular, we consider the setting of coevolutionary simulations whereby the primary motivations in studies will be on the dynamics of coevolutionary processes. We will present studies we have carried out to understand coevolutionary processes using tools from dynamical systems theory. By targeting analysis on population dynamics, they can be formulated within an evolutionary game theoretic setup as a family of one-dimensional discrete-time dynamical system. This lets us investigate the relationship between simulations and mathematical models from two perspectives: (i) Whether computer-generated pseudo-trajectories are faithfully informative of underlying dynamics. (ii) Whether the models reflect the natural system that generate trajectories limited by finite-population effects. We focus on the Shadowing property of those dynamical systems. For first perspective, we use an isolated fixed point argument to show that there is no Shadowing property. Most of the dynamical maps constructed from selection operators used in coevolutionary systems have a discontinuous fixed point. For the second perspective, we focus on a family of smooth, nonlinear, bimodal dynamical maps that might be hyperbolic and structurally stable, for which the Shadowing property can be demonstrated. We provide a positive indication via direct calculations that these maps have negative Schwarzian derivatives.