Concept explainers
The sudden outbreak of an insect population can be modeled by the equation
The first term relates to the well-known logistic population growth model where N is the number of insects. R is an intrinsic growth rate, and C is the carrying capacity of the local environment. The second term represents the effects of bird predation. Its effect becomes significant when the population reaches a critical size Nc; r is the maximum value that the second term can reach at large values of N.
Solve the differential equation for
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