What is the logistic map in population biology?

The logistic map is a discrete dynamical system defined by a polynomial mapping of degree two that serves as a simple demographic model. Popularized in biology by Robert May in 1976 as an analogue to Pierre François Verhulst's continuous logistic equation, it demonstrates how complex, chaotic behavior can emerge from simple nonlinear equations.

What we know

• The logistic map is classified as a recurrence relation and a polynomial mapping of degree 2 that exhibits chaotic behavior. [1, 2]
• Biologist Robert May popularized the logistic map in a 1976 paper as a discrete-time demographic model analogous to Pierre François Verhulst's logistic equation. [2]
• The map serves as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations. [2]
• Edward Lorenz initially used the map in the 1960s to showcase properties of irregular solutions in climate systems. [2]

Where to go next

• whoWho was Robert May?
• compared withWhat is the continuous logistic equation?
• the bigger pictureHow does chaos theory apply to dynamical systems?
• how it workedWhat is a recurrence relation?
• how we knowHow did Edward Lorenz study climate systems?
• an unexpected connectionHow does a population model relate to climate systems?The same mathematical map used to model discrete population biology was initially used by Edward Lorenz in the 1960s to study irregular solutions in weather and climate systems.

Sources

• [1]logistic map (Wikidata Q587182) · CC0 1.0
• [2]Logistic map · CC BY-SA 4.0
• [3]Logistic function · CC BY-SA 4.0
• [4]Logistic regression · CC BY-SA 4.0
• [5]Outline of biology · CC BY-SA 4.0