3. The survival of two species depends on their mutual cooperation. For instance, a species of bee that feeds primarily on the nectar of one plant species and simultaneously pollinates the plant. One simple model of mutualism is given by dr = -ax + bay xt dy = -my + nxy dt where a, b, m, and n are all positive constants. (a) What assumptions are implicitly being made about the growth of each species in the absence of cooperation? (b) Interpret the constants a, b, m, and n in terms of the physical problem.

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Chapter2: Second-order Linear Odes
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3. The survival of two species depends on their mutual cooperation. For instance, a species
of bee that feeds primarily on the nectar of one plant species and simultaneously pollinates
the plant. One simple model of mutualism is given by
dx
-ax + bry
xt
dy
= -my + nxy
dt
where a, b, m, and n are all positive constants.
(a) What assumptions are implicitly being made about the growth of each species in the
absence of cooperation?
(b) Interpret the constants a, b, m, and n in terms of the physical problem.
Transcribed Image Text:3. The survival of two species depends on their mutual cooperation. For instance, a species of bee that feeds primarily on the nectar of one plant species and simultaneously pollinates the plant. One simple model of mutualism is given by dx -ax + bry xt dy = -my + nxy dt where a, b, m, and n are all positive constants. (a) What assumptions are implicitly being made about the growth of each species in the absence of cooperation? (b) Interpret the constants a, b, m, and n in terms of the physical problem.
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