(a) Explanation Given information: To model a population with a differential equation of the form d P d t = f ( P ) , where P(t) is the population at time t. The experiments have been performed on the population that gives the following information as, The only equilibrium points in the population are P=0, P=10 and P=50. If the population is 100, the population decreases. If the population is 25, the population increases. Calculation: The model positively describes the population between 25 and 100.But the behavior between 0 and 25 has not been described at all, except there is an equilibrium position for p=10. This leads to two possibilities, Between 0 and 10 it is decreasing Between 0 and 10 it is increasing There are two phase portraits possible, I : 0 < P < 10 ↓ 10 < P < 50 ↑ 50 < p < 100 ↓ I I : 0 < P < 10 ↑ 10 < P < 50 ↑ (b) To determine To sketch: the corresponding function f(P) for each of the phase lines. (c) To determine To find: the formula for functions f(P) whose graph agrees qualitively with the rough sketches in part(b) for each of your phase lines.

4th Edition

ISBN: 9780495562009

Author: Blanchard Devaney Gl

Publisher: Cengage Learning

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Differential Equations

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Chapter 1.6, Problem 39E

(a)

To determine

To sketch: the possible phase lines for the system for P>0 since there are two.

(b)

To determine

To sketch:the corresponding function f(P) for each of the phase lines.

(c)

To determine

To find:the formula for functions f(P) whose graph agrees qualitively with the rough sketches in part(b) for each of your phase lines.

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Chapter 1.6, Problem 38E

Chapter 1.6, Problem 40E

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the possible phase lines for the system for P&gt;0 since there are two.

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To sketch: the possible phase lines for the system for P>0 since there are two.

To sketch:the corresponding function f(P) for each of the phase lines.

To find:the formula for functions f(P) whose graph agrees qualitively with the rough sketches in part(b) for each of your phase lines.

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Chapter 1 Solutions

the possible phase lines for the system for P>0 since there are two.