Determine the types of each equilibrium point

Reference no: EM13895765

1. Give an example of a nonlinear system that has an equilibrium point for which the linearized system has a zero eigenvalue, but the nonlinear system has only one equilibrium point.

2. For the system

x' = y - 1
y' = y - x2,

determine the types of each equilibrium point.

3. For the system

x' = sin(x)
y' = cos(y),

find all equilibrium points and use linearization together with the nullclines to sketch the phase plane.

Reference no: EM13895765

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