Delayed Logistic Equation or Hutchinson\'s Equation: The delayed logistic equation was first
proposed by Hutchinson in 1948. Hutchinson was studying the growth of the species Daphnia, a
small, planktonic crustacean, commonly known as the water flea. Assuming that the process of
reproduction is not instantaneous, he modeled their growth using the logistic equation as dD/dt
= r D(t) [1 - D(t - tau)/k] where tau(> 0) is the discrete time delay because of the time taken for
egg formation before hatching, r is the intrinsic growth rate and k is the carrying capacity. Find
the steady state(s) of the model. Solve the DDE numerically, taking r = 0.15, k = 1.00, tau = 8
and initial history to be 0.5. What conclusion(s) do you draw for tau = 8 and tau = 11?
Solution
https://en.wikipedia.org/wiki/Delay_differential_equation.
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Delayed Logistic Equation or Hutchinsons Equation The delayed logi.pdf
1. Delayed Logistic Equation or Hutchinson's Equation: The delayed logistic equation was first
proposed by Hutchinson in 1948. Hutchinson was studying the growth of the species Daphnia, a
small, planktonic crustacean, commonly known as the water flea. Assuming that the process of
reproduction is not instantaneous, he modeled their growth using the logistic equation as dD/dt
= r D(t) [1 - D(t - tau)/k] where tau(> 0) is the discrete time delay because of the time taken for
egg formation before hatching, r is the intrinsic growth rate and k is the carrying capacity. Find
the steady state(s) of the model. Solve the DDE numerically, taking r = 0.15, k = 1.00, tau = 8
and initial history to be 0.5. What conclusion(s) do you draw for tau = 8 and tau = 11?
Solution
https://en.wikipedia.org/wiki/Delay_differential_equation
![Delayed Logistic Equation or Hutchinson's Equation: The delayed logistic equation was first
proposed by Hutchinson in 1948. Hutchinson was studying the growth of the species Daphnia, a
small, planktonic crustacean, commonly known as the water flea. Assuming that the process of
reproduction is not instantaneous, he modeled their growth using the logistic equation as dD/dt
= r D(t) [1 - D(t - tau)/k] where tau(> 0) is the discrete time delay because of the time taken for
egg formation before hatching, r is the intrinsic growth rate and k is the carrying capacity. Find
the steady state(s) of the model. Solve the DDE numerically, taking r = 0.15, k = 1.00, tau = 8
and initial history to be 0.5. What conclusion(s) do you draw for tau = 8 and tau = 11?
Solution
https://en.wikipedia.org/wiki/Delay_differential_equation](https://image.slidesharecdn.com/delayedlogisticequationorhutchinsonsequationthedelayedlogi-230702085623-52e250b5/85/Delayed-Logistic-Equation-or-Hutchinsons-Equation-The-delayed-logi-pdf-1-320.jpg)
