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
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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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