By direct calculation show that (using polar coordianted) that $$ \dot x=x-y-x(x²+y²) $$
$$ \dot y=x+y-y(x²+y²) $$
Show that this has a limit cycle
I need help understanding how to test whether it is a limit cycle or not. Do we check whether $$ f_x+g_y=0? $$ I am not sure whether this should be done once it is converted to polar series or before. Nor can I find a proper source about "how to test whether a system is a limit cycle" on the web. Any help will do thx!