The Lotka-Volterra equations are often used to model the links between a particular population of prey organisms and a population of predatory organisms. In a particular ecosystem u is used to represent the number of predatory organisms and v to represent the number of prey organisms. Suppose the growth rate uv of the predatory organisms is f(u,v) = - 0.5u + and of the prey organisms is g(u,v) = 6v – 10uv. 100 (a) Show that if u = 0.6 and v = 50, then f (u,v) = 0, and g(u,v) = 0. (The populations are said to be in equilibrium.) f(u,v) (b) Find the linear approximation of the vector valued function h:(u,v)→ if u is close to 0.6 and v is g(u,v) close to 50. ..... (a) Evaluate f(u,v) at u = 0.6 and v = 50, f(0.6, 50) =. (Type an integer.)
The Lotka-Volterra equations are often used to model the links between a particular population of prey organisms and a population of predatory organisms. In a particular ecosystem u is used to represent the number of predatory organisms and v to represent the number of prey organisms. Suppose the growth rate uv of the predatory organisms is f(u,v) = - 0.5u + and of the prey organisms is g(u,v) = 6v – 10uv. 100 (a) Show that if u = 0.6 and v = 50, then f (u,v) = 0, and g(u,v) = 0. (The populations are said to be in equilibrium.) f(u,v) (b) Find the linear approximation of the vector valued function h:(u,v)→ if u is close to 0.6 and v is g(u,v) close to 50. ..... (a) Evaluate f(u,v) at u = 0.6 and v = 50, f(0.6, 50) =. (Type an integer.)
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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Transcribed Image Text:The Lotka-Volterra equations are often used to model the links between a particular population of prey
organisms and a population of predatory organisms. In a particular ecosystem u is used to represent the
number of predatory organisms and v to represent the number of prey organisms. Suppose the growth rate
uv
of the predatory organisms is f(u,v) = - 0.5u +
and of the prey organisms is g(u,v) = 6v – 10uv.
100
(a) Show that if u = 0.6 and v = 50, then f (u,v) = 0, and g(u,v) = 0. (The populations are said to be in
equilibrium.)
%D
%3D
f(u,v)
(b) Find the linear approximation of the vector valued function h:(u,v)→
if u is close to 0.6 and v is
g(u,v)
close to 50.
(a) Evaluate f(u,v) at u = 0.6 and v = 50, f(0.6, 50) =
(Type an integer.)
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