The system of differential equations dx/dt = 0.4x − 0.002x2 − 0.001xy dy/dt = 0.6y − 0.001y2 − 0.007xy   is a model for the populations of two species.   (a) Does the model describe cooperation, or competition, or a predator-prey relationship? competition cooperation    predator-prey relationship (b) Find the equilibrium solutions. (Enter solutions from smallest to largest value of x. If solutions have the same value of x, enter them from smallest to largest y.) (x,y) = (_______) (x,y) = (_______) (x,y) = (_______) (x,y) = (_______)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The system of differential equations

dx/dt = 0.4x − 0.002x2 − 0.001xy

dy/dt = 0.6y − 0.001y2 − 0.007xy

 

is a model for the populations of two species.

 

(a) Does the model describe cooperation, or competition, or a predator-prey relationship?

competition

cooperation   

predator-prey

relationship

(b) Find the equilibrium solutions. (Enter solutions from smallest to largest value of x. If solutions have the same value of x, enter them from smallest to largest y.)

(x,y) = (_______)

(x,y) = (_______)

(x,y) = (_______)

(x,y) = (_______)

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