Suppose the densities of two species evolve in accordance with the LotkaVolterra model

Chapter 11, Problem 2

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Suppose the densities of two species evolve in accordance with the LotkaVolterra model of interspecific competition. Assume that species 1 has intrinsic rate of growth r1 = 4 and carrying capacity K1 = 17 and that species 2 has intrinsic rate of growth r2 = 1.5 and carrying capacity K2 = 32. Furthermore, assume that 15 individuals of species 2 have the same effect on species 1 as 7 individuals of species 1 have on themselves and that 5 individuals of species 1 have the same effect on species 2 as 7 individuals of species 2 have on themselves. Find a system of differential equations that describes this situation.

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