opulation equilibria can be stable or unstable. If, when a population deviates a bit from the equilibrium value (as populations inevitably do), it tends to return to it, this is a stable equilibrium; if, however, when the population deviates om the equilibrium it tends to diverge from it even further, this is an unstable equilibrium. hink of a ball in the pocket of a snooker table versus a ball balanced on a snooker cue. Unstable equilibria are a feature of Allee effect models such as the following. se a phase portrait of the autonomous equation above to determine whether the nonzero equilibria that you found in question (2) are stable or unstable. (Hint: See Section 2.1 of the text. List the equilibria according to their stability. nter your answers as comma-separated lists. If there are no equilibria in a certain category, enter NONE.) able
opulation equilibria can be stable or unstable. If, when a population deviates a bit from the equilibrium value (as populations inevitably do), it tends to return to it, this is a stable equilibrium; if, however, when the population deviates om the equilibrium it tends to diverge from it even further, this is an unstable equilibrium. hink of a ball in the pocket of a snooker table versus a ball balanced on a snooker cue. Unstable equilibria are a feature of Allee effect models such as the following. se a phase portrait of the autonomous equation above to determine whether the nonzero equilibria that you found in question (2) are stable or unstable. (Hint: See Section 2.1 of the text. List the equilibria according to their stability. nter your answers as comma-separated lists. If there are no equilibria in a certain category, enter NONE.) able
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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Question
![Population equilibria can be stable or unstable. If, when a population deviates a bit from the equilibrium value (as populations inevitably do), it tends to return to it, this is a stable equilibrium; if, however, when the population deviates
from the equilibrium it tends to diverge from it even further, this is an unstable equilibrium.
Think of a ball in the pocket of a snooker table versus a ball balanced on a snooker cue. Unstable equilibria are a feature of Allee effect models such as the following.
dN
Use a phase portrait of the autonomous equation above to determine whether the nonzero equilibria that you found in question (2) are stable or unstable. (Hint: See Section 2.1 of the text. List the equilibria according to their stability.
Enter your answers as comma-separated lists. If there are no equilibria in a certain category, enter NONE.)
stable
N =
unstable
N =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88ca13b2-e90a-4f8b-aa87-163472e135e3%2Fd92f6424-af47-4a63-899c-355122434656%2Fxqtadps_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Population equilibria can be stable or unstable. If, when a population deviates a bit from the equilibrium value (as populations inevitably do), it tends to return to it, this is a stable equilibrium; if, however, when the population deviates
from the equilibrium it tends to diverge from it even further, this is an unstable equilibrium.
Think of a ball in the pocket of a snooker table versus a ball balanced on a snooker cue. Unstable equilibria are a feature of Allee effect models such as the following.
dN
Use a phase portrait of the autonomous equation above to determine whether the nonzero equilibria that you found in question (2) are stable or unstable. (Hint: See Section 2.1 of the text. List the equilibria according to their stability.
Enter your answers as comma-separated lists. If there are no equilibria in a certain category, enter NONE.)
stable
N =
unstable
N =
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