Discrete Dynamics in Nature and Society

Discrete Dynamics in Nature and Society / 2005 / Article

Open Access

Volume 2005 |Article ID 253208 | https://doi.org/10.1155/DDNS.2005.87

Terence R. Blows, Barry J. Wimmer, "A simple mathematical model for Batesian mimicry", Discrete Dynamics in Nature and Society, vol. 2005, Article ID 253208, 6 pages, 2005. https://doi.org/10.1155/DDNS.2005.87

A simple mathematical model for Batesian mimicry

Received24 Sep 2003

Abstract

A simple mathematical model is presented for Batesian mimicry, which occurs when a harmless species (mimic) is morphologically similar to another species (model) that is noxious or distasteful to predators, thus gaining a measure of protection. Although mathematical models for species interaction, such as predator-prey or competition, are well known, there is no similar literature on mimicry. The mathematical model developed here is a one-dimensional iterated map which has the full range of dynamic behavior present in the logistic map, depending on the values of its parameters. The dynamics ranges from a stable fixed point and stable cycles through chaotic dynamics achieved through a sequence of period doubling bifurcations.

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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