Logistic map

The logistic map is a polynomial mapping, often cited as an archetypical example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a seminal 1976 paper by the biologist Robert May. The logistic model was originally introduced as a demographic model by Pierre François Verhulst. Later it was applied on surplus production of the population biomass of species in the presence of limiting factors such as food supply or disease, and so two causal effects:

Related Topics:
Polynomial - Chaotic - Non-linear - 1976 - Robert May - Demographic - Model - Pierre François Verhulst - Surplus production - Population - Biomass - Species - Limiting factor

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• reproduction means the population will increase at a rate proportional to the current population
• starvation means the population will decrease at a rate proportional to the value obtained by taking the theoretical "carrying capacity" of the environment less the current population.

Mathematically this can be written as

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:

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(1)qquad x_{n+1} = r x_n (1-x_n)

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where:

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:x_n is a number between zero and one, and represents the population at year n, and hence x0 represents the initial population (at year 0)

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:r is a positive number, and represents a combined rate for reproduction and starvation.

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Logistic map: Behaviour dependent on r ►