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2. Consider the following quadratic population model where (1,15 > 0. Here {10:2 represents the death due to overcrowding (that is1 death rate is
proportional to 3:2 due to the interaction of the population with itself). (3') Find all the equilibrium points and determine their stability. (33') Show that this model is exactly the same as the logistic model by expressing the con—
stants a and b in terms of the intrinsic growth rate r and carrying capacity K.

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2 i dx/dt = a x - b x 2 = a ( x ) ( 1 - b x/a ) for equilibrium , dx/dt = 0 , a ( x ) ( 1 - b x/a ) = 0 , equilibrium pints x... View the full answer

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