Delayed Logistic Equation or Hutchinson\'s Equation: The delayed logistic equati

Question

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?

Explanation / Answer

https://en.wikipedia.org/wiki/Delay_differential_equation

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