13.In the Lotka–Volterra equations, the interaction between the two species is modeled by terms proportional to the product xy of the respective populations. If the prey population is much larger than the predator population, this may overstate the interaction; for example, a predator may hunt only when it is hungry and ignore the prey at other times. In this problem we consider an alternative model proposed by Rosenzweig and MacArthur.10 a.Consider the system x′=x(1−x5−2yx+6),y′=y(−14+xx+6).x′=x1−x5−2yx+6,y′=y−14+xx+6. Find all of the critical points of this system. b.Determine the type and stability characteristics of each critical point.
13.In the Lotka–Volterra equations, the interaction between the two species is modeled by terms proportional to the product xy of the respective populations. If the prey population is much larger than the predator population, this may overstate the interaction; for example, a predator may hunt only when it is hungry and ignore the prey at other times. In this problem we consider an alternative model proposed by Rosenzweig and MacArthur.10 a.Consider the system x′=x(1−x5−2yx+6),y′=y(−14+xx+6).x′=x1−x5−2yx+6,y′=y−14+xx+6. Find all of the critical points of this system. b.Determine the type and stability characteristics of each critical point.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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13.In the Lotka–Volterra equations, the interaction between the two species is modeled by terms proportional to the product xy of the respective populations. If the prey population is much larger than the predator population, this may overstate the interaction; for example, a predator may hunt only when it is hungry and ignore the prey at other times. In this problem we consider an alternative model proposed by Rosenzweig and MacArthur.10
a.Consider the system
x′=x(1−x5−2yx+6),y′=y(−14+xx+6).x′=x1−x5−2yx+6,y′=y−14+xx+6.
Find all of the critical points of this system.
b.Determine the type and stability characteristics of each critical point.
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