Elizabeth Wesson

ROUNDNESS PROPERTIES OF ULTRAMETRIC SPACES

We obtain several new characterizations of ultrametric spaces in terms of roundness, generalized roundness, strict p-negative type, and p-polygonal equalities (p > 0). This allows new insight into the isometric embedding of ultrametric spaces into Euclidean spaces. We also consider roundness properties additive metric spaces which are not ultrametric.

Hopf Bifurcations in Two-Strategy Delayed Replicator Dynamics

We investigate the dynamics of two-strategy replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval T. We analyze two models: in the first, all terms in the fitness are delayed, while in the second, only opposite-strategy terms are delayed. We compare the two models via a linear homotopy. Taking the delay T as a bifurcation parameter, we demonstrate the existence of (nondegenerate) Hopf bifurcations in both models, and present an analysis of the resulting limit cycles using Lindstedt’s method.

Hopf Bifurcations in Delayed Rock-Paper-Scissors Replicator Dynamics

We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval

Alternate Models of Replicator Dynamics

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An analysis of queues with delayed information and time-varying arrival rates

T. Taking

Classifications of ultrametric spaces according to roundness

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