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Supposethat the system of differential equations describing a particular predator-prey model is given by dx/dt = 10-2 x - 2×10-5 xy; dy/dt = -4×10-2 y +10-5 xy where y and x are the numbers of predator and prey, respectively, and t is the time in days.  (a) Determinethe numbers of predator and prey at equilibrium. (b) Write the equations of the phase curves in the neighborhood of the equilibrium point

Supposethat the system of differential equations describing a particular predator-prey model is given by dx/dt = 10-2 x - 2×10-5 xy; dy/dt = -4×10-2 y +10-5 xy where y and x are the numbers of predator and prey, respectively, and t is the time in days.  (a) Determinethe numbers of predator and prey at equilibrium. (b) Write the equations of the phase curves in the neighborhood of the equilibrium point

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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Supposethat the system of differential equations describing a particular predator-prey model is given by

dx/dt = 10-2 x - 2×10-5 xy; dy/dt = -4×10-2 y +10-5 xy where y and x are

the numbers of predator and prey, respectively, and t is the time in days. 

(a) Determinethe numbers of predator and prey at equilibrium.

(b) Write the equations of the phase curves in the neighborhood of the equilibrium point.

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