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Consider the Lotka-Volterra predator-prey model defined by = -0.1х + 0.02ху = 0.2y - 0.025ху, where the populations x(t) (predators) and y(t) (prey) are measured in thousands. Suppose x(0) = 6 and y(0) = 6. Use a numerical solver to graph x(t) and y(t). x, y x, y 10 10- Уул уу М кам x,y 10 500 1000 О Use the graphs to approximate the time t> 0 when the two populations are first equal. 500 1000 Use the graphs to approximate the period of each population. period of x period of y t x, y 10 50 100 50 ^^ . 100 t

Consider the Lotka-Volterra predator-prey model defined by = -0.1х + 0.02ху = 0.2y - 0.025ху, where the populations x(t) (predators) and y(t) (prey) are measured in thousands. Suppose x(0) = 6 and y(0) = 6. Use a numerical solver to graph x(t) and y(t). x, y x, y 10 10- Уул уу М кам x,y 10 500 1000 О Use the graphs to approximate the time t> 0 when the two populations are first equal. 500 1000 Use the graphs to approximate the period of each population. period of x period of y t x, y 10 50 100 50 ^^ . 100 t

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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Consider the Lotka-Volterra predator-prey model defined by = -0.1x + 0.02xy = 0.2У - 0.025ХУ, where the populations x(t) (predators) and y(t) (prey) are measured in thousands. Suppose x(0) = 6 and y(0) = 6. Use a numerical solver to graph x(t) and y(t). x, y x, y 10 10- ки ки 500 1000 t x, y x, y 10 10 ними жи Use the graphs to approximate the period of each population. period of x period of y t 500 1000 0 Use the graphs to approximate the time t> 0 when the two populations are first equal. 50 50 100 100 t
Transcribed Image Text:Consider the Lotka-Volterra predator-prey model defined by = -0.1x + 0.02xy = 0.2У - 0.025ХУ, where the populations x(t) (predators) and y(t) (prey) are measured in thousands. Suppose x(0) = 6 and y(0) = 6. Use a numerical solver to graph x(t) and y(t). x, y x, y 10 10- ки ки 500 1000 t x, y x, y 10 10 ними жи Use the graphs to approximate the period of each population. period of x period of y t 500 1000 0 Use the graphs to approximate the time t> 0 when the two populations are first equal. 50 50 100 100 t
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