(Non-Uniform Oscillators) (Strogatz 4.3.3, 13 points) For the vector field on the circle = sin() sin(2),find the fixed points and draw the flow on the circle assuming 0. Do the cases 2, = 2, 0 2 and = 0 separately. (Hint: expand sin(2).) (Strogatz 4.5.3 (a) only, 6 points) Show that = + sin(), where is slightly lessthan 1, is an excitable system. That is, it satisfies two properties: it has a uniqueglobally attracting rest state; and a large enough stimulus can send the system ona long excursion until it returns to the rest state. What is the rest state? Andwhat threshold do you have to overcome with a stimulus to send the system on theexcursion? Hint: draw the flow on the circle.