### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 87-92 |

Number of pages | 6 |

Journal | Discrete Dynamics in Nature and Society |

Volume | 2005 |

Issue number | 1 |

DOIs | |

State | Published - Jan 12 2005 |

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### ASJC Scopus subject areas

- General
- Modeling and Simulation

### Cite this

*Discrete Dynamics in Nature and Society*,

*2005*(1), 87-92. https://doi.org/10.1155/DDNS.2005.87

**A simple mathematical model for Batesian mimicry.** / Blows, Terence R; Wimmer, Barry J.

Research output: Contribution to journal › Article

*Discrete Dynamics in Nature and Society*, vol. 2005, no. 1, pp. 87-92. https://doi.org/10.1155/DDNS.2005.87

}

TY - JOUR

T1 - A simple mathematical model for Batesian mimicry

AU - Blows, Terence R

AU - Wimmer, Barry J.

PY - 2005/1/12

Y1 - 2005/1/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21044445461&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21044445461&partnerID=8YFLogxK

U2 - 10.1155/DDNS.2005.87

DO - 10.1155/DDNS.2005.87

M3 - Article

VL - 2005

SP - 87

EP - 92

JO - Discrete Dynamics in Nature and Society

JF - Discrete Dynamics in Nature and Society

SN - 1026-0226

IS - 1

ER -