Population dynamics: single species: chaotic

Model : chaos
Simile version : 3.1+
Date added : 2003-09-11
Keywords : Population dynamics ; Single-species population dynamics ; Chaotic behaviour ;

Description

This version differs from the standard population model in two respects:

1. the growth rate depends on the current population by a quadratic relation. This will cause the population to approach the point of zero growth; and
2. we consider time as being discrete rather than continuous. Rather than using a very small time increment between model states it is set equal to the time unit.

The behaviour of this model approximates that of a population where new individuals arrive all at once at a certain time of year, and most deaths also occur within a short period each year.

X(t+1) = g X(t) (1 - X(t)/100)
where:
X(t) = population size (number of individuals, or number of individuals per unit area) at time t g = growth rate (number of new individuals for each existing one with no resource constraints)

Files

Model file Click on the icon to download the model file. (You will need Simile to examine and run the model. A free evaluation version is available from the products page.) Some browsers may attempt to display the model file, rather than open it in Simile; in this case, use the browser back button to return to this page, and use the context menu (invoked by right-clicking on the link) to save the target file to disk.

chaos.sml

Equations

Compartment   level
	Initial value = rand_const(50,50.000001)
	Rate of change =  + change
 
Flow   change
	change = gain*level*(1-level/100)