Answer Happy

(a)Determine all of the critical points of the non-linear
system.
(b)For each of the critical points in part (a):
i.Determine the linearised system.
ii.Discuss whether the linearised system can be used to approximate
the behaviour of the
non-linear system.
(c)For the linearised system(s)with real eigenvalues:
(i)Determine the general solution of the linearised system using
eigenvalues and eigenvec-
tors.
(ii)Determine the type and stability of the critical point.
Consider the non-linear first order system: 1-Y dx dt dy dt sin(x+y) (a) Determine all of the critical points of the non-linear system. (b) For each of the critical points in part (a): i. Determine the linearised system. ii. Discuss whether the linearised system can be used to approximate the behaviour of the non-linear system. (c) For the linearised system(s) with real eigenvalues: (i) Determine the general solution of the linearised system using eigenvalues and eigenvec- tors. (ii) Determine the type and stability of the critical point.