Delay Logistic Equation
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This shows the solution of the scalar delay logistic equation 
in blue along with the solution of the logistic equation without delay (
) in red.
Contributed by: Rob Knapp (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
For 
, solutions are monotonic. For 
, the solutions are oscillatory and asymptotically approach 
. For 
, the solutions approach a limit cycle. The boundaries can be determined by considering the test solution 
, which gives the equation 
; that has the solution 
, where 
is the ProductLog function.
Reference: K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Boston: Kluwer, 1992.
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