Freely forming groups: trying to be rare

Baake, Michael; Grimm, Uwe and Jockusch, Harald (2006). Freely forming groups: trying to be rare. The ANZIAM Journal, 48 pp. 1–10.

URL: http://www.austms.org.au/Publ/Jamsb/V48P1/2382.htm...

Abstract

A simple weakly frequency dependent model for the dynamics of a population with a finite number of types is proposed, based upon an advantage of being rare. In the infinite population limit, this model gives rise to a non-smooth dynamical system that reaches its globally stable equilibrium in finite time. This dynamical system is sufficiently simple to permit an explicit solution, built piecewise from solutions of the logistic equation in continuous time. It displays an interesting tree-like structure of coalescing components.

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About

• Item ORO ID
• 5817
• Item Type
• Journal Item
• ISSN
• 1446-1811
• Extra Information
• Preprint version q-bio/0509011 available at http://arxiv.org/abs/q-bio/0509011
• Keywords
• population dynamics; non-smooth dynamical systems; stable equilibria; logistic equation
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Uwe Grimm