Need help in non-linear dynamics problem

Question

johnweldon1993 · Answer

Post it up!

osprey · Answer

Is it an question about a stealth aircraft made invisible ?

jango_in_dtown · Answer

Locate the critical points and find their nature for the following non-linear system

jango_in_dtown · Answer

$$dx/dt= 4-4x^2-y^2$$

jango_in_dtown · Answer

dy/dt=3xy

jango_in_dtown · Answer

for critical points, dx/dt=0 and dy/dt=0

irishboy123 · Answer

**linearise**

jango_in_dtown · Answer

solving i got (0,2), (0,-2), (1,0) and (-1,0) as critical points

jango_in_dtown · Answer

taking the point (0,2) and linearizing I got the critical point as a centre

jango_in_dtown · Answer

But dont know what will be the corrsponding nature for the non-linear system

irishboy123 · Answer

ah!!  

so you've been told that linearisation does not necessarily work for centres?

jango_in_dtown · Answer

Poncare's theroem

jango_in_dtown · Answer

It says that if the linear approximation has a centre, then the non-linear system can either be a centre or a spiral

irishboy123 · Answer

yeah

i did non-lin DE's recently and got into the [bad] habit of losing a few marks on that very point.

i have some notes somewhere that purport to address the point.  but they never made that much sense at the time so i took a view

i'll dig them out later

irishboy123 · Answer

and i'm wondering out loud whether, with that many CP's, you can just work it out from the other bits of the phase portrait.

bit rusty.

jango_in_dtown · Answer

Yes thanks for the help..

irishboy123 · Answer

|dw:1474109596386:dw|

this is all i can find in terms of notes right now, and it's not that helpful