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A predator-prey interaction is described by the Lotka-Volterra model x'= -0.3x + 0.04xy y' = 0.4y -0.04xy. (a) Find the critical point in the first quadrant. (x, y) = ([ Use a numerical solver to sketch some population cycles. (Choose x(0) = 9 and y(0) = 6.) 14 14 12 X(t) 12 x(t) 10 10 8 8 6 4y(t) 40 100 12 X(t)/ 10 www 4-y(t) 2 t 20 40 60 80 100 fy(t) 2 10 4y(t) 2 20 20 40 100 M 60 80 100

A predator-prey interaction is described by the Lotka-Volterra model x'= -0.3x + 0.04xy y' = 0.4y -0.04xy. (a) Find the critical point in the first quadrant. (x, y) = ([ Use a numerical solver to sketch some population cycles. (Choose x(0) = 9 and y(0) = 6.) 14 14 12 X(t) 12 x(t) 10 10 8 8 6 4y(t) 40 100 12 X(t)/ 10 www 4-y(t) 2 t 20 40 60 80 100 fy(t) 2 10 4y(t) 2 20 20 40 100 M 60 80 100

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A predator-prey interaction is described by the Lotka-Volterra model x'= -0.3x + 0.04xy y' = 0.4y -0.04xy. (a) Find the critical point in the first quadrant. (x, y) = ( Use a numerical solver to sketch some population cycles. (Choose x(0) = 9 and y(0) = 6.) 14 14 12 X(t) 12 X(t) 10 10 8 6 40 y(t) 2 20 10 N 4y(t) 2 20 40 100 M и 60 80 100 8 4y(t) 80 100 12 X(t)/ 10 www 4y(t) 2 20 40 60 80 100
Transcribed Image Text:A predator-prey interaction is described by the Lotka-Volterra model x'= -0.3x + 0.04xy y' = 0.4y -0.04xy. (a) Find the critical point in the first quadrant. (x, y) = ( Use a numerical solver to sketch some population cycles. (Choose x(0) = 9 and y(0) = 6.) 14 14 12 X(t) 12 X(t) 10 10 8 6 40 y(t) 2 20 10 N 4y(t) 2 20 40 100 M и 60 80 100 8 4y(t) 80 100 12 X(t)/ 10 www 4y(t) 2 20 40 60 80 100
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