Recall that cos(x) = cos(x-л) and consider the differential equation on the domain xЄ [0,л], у Є [0,л]. d dt x(t) = − sin(x) (cos(x) + cos(y)) Then, d ty(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 xЄ [0,л], у Є [0,л]. d dt x(t) = − sin(x) (cos(x) + cos(y)) Then, d ty(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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can you please show the sketches and the mathematical working out
![Recall that cos(x) = cos(x-л) and consider the differential equation on the domain
xЄ [0,л], у Є [0,л].
d
dt
x(t) = − sin(x) (cos(x) + cos(y))
Then,
d
ty(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%2Fabb569d5-7994-45b7-80e0-a9312d04c3d0%2Fregjix_processed.png&w=3840&q=75)
Transcribed Image Text:Recall that cos(x) = cos(x-л) and consider the differential equation on the domain
xЄ [0,л], у Є [0,л].
d
dt
x(t) = − sin(x) (cos(x) + cos(y))
Then,
d
ty(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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