Recall that cos(x) = cos(x-л) and consider the differential equation on the domain x Є [0,л], у Є [0,π]. d x(t) = = sin(x) (cos(x)+cos(y)) Then, d dt (t) = sin(y) (cos(x) — cos(y)) • sketch the 6 nullclines of the differential equation in this region, • determine any equilibria, ⚫ determine the linear stability of equilibria points using the Jacobian matrix.
Recall that cos(x) = cos(x-л) and consider the differential equation on the domain x Є [0,л], у Є [0,π]. d x(t) = = sin(x) (cos(x)+cos(y)) Then, d dt (t) = sin(y) (cos(x) — cos(y)) • sketch the 6 nullclines of the differential equation in this region, • determine any equilibria, ⚫ determine the linear stability of equilibria points using the Jacobian matrix.
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
![Recall that cos(x) = cos(x-л) and consider the differential equation on the domain
x Є [0,л], у Є [0,π].
d
x(t) = = sin(x) (cos(x)+cos(y))
Then,
d
dt
(t) = sin(y) (cos(x) — cos(y))
•
sketch the 6 nullclines of the differential equation in this region,
• determine any equilibria,
⚫ determine the linear stability of equilibria points using the Jacobian matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4061eb31-6ba2-4539-9b51-dd7b05481e7e%2Fd233399f-6af8-47b4-87c6-5a3e520cf9ed%2Fyqflmj9_processed.png&w=3840&q=75)
Transcribed Image Text:Recall that cos(x) = cos(x-л) and consider the differential equation on the domain
x Є [0,л], у Є [0,π].
d
x(t) = = sin(x) (cos(x)+cos(y))
Then,
d
dt
(t) = sin(y) (cos(x) — cos(y))
•
sketch the 6 nullclines of the differential equation in this region,
• determine any equilibria,
⚫ determine the linear stability of equilibria points using the Jacobian matrix.
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