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# Consider the nonlinear system of differential equationsdxdy d =y-e"1y - TyDetermine all critical points of the system: For each critical point not on the y-axi...

## Question

###### Consider the nonlinear system of differential equationsdxdy d =y-e"1y - TyDetermine all critical points of the system: For each critical point not on the y-axis: Determine the linearisation of the system with the critical point translated to (0,0) and discuss whether it can be used to approximate the behaviour of the non-linear system Find the general solution of the linearised system using eigenvalues and eigenvectors. Sketch by hand the phase portrait of the linearised system_ Include all

Consider the nonlinear system of differential equations dx dy d =y-e" 1y - Ty Determine all critical points of the system: For each critical point not on the y-axis: Determine the linearisation of the system with the critical point translated to (0,0) and discuss whether it can be used to approximate the behaviour of the non-linear system Find the general solution of the linearised system using eigenvalues and eigenvectors. Sketch by hand the phase portrait of the linearised system_ Include all working of any special cases corresponding to straight line orbits behaviour of general orbits as and t and slopes of orbits across the axes Identify the type and stability of the critical point of the linearised system Using PPLANE, produce global phase portrait of the non-linear system in a region that includes all of the critical points_ The phase portrait should illustrate the behaviour of orbits in the vicinity of each critical point.

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