Consider the differential equation '=ry + 4y, where r is a parameter. a. [4pts] Find the...

 

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Consider the differential equation '=ry + 4y, where r is a parameter. a. [4pts] Find the value r, such that bifurcation occurs at r = Tb. b. [8pts] Draw the function on the right hand side of the differential equation (in the (3',y) plane) in 3 different regimes: r r. In each regime, find the fixed points, draw the flow arrows on the y-axis and indicate the stability of each fixed point. c. [8pts] Draw the bifurcation diagram. Use dashed lines for unstable fixed points and solid lines for the stable ones. Consider the differential equation '=ry + 4y, where r is a parameter. a. [4pts] Find the value r, such that bifurcation occurs at r = Tb. b. [8pts] Draw the function on the right hand side of the differential equation (in the (3',y) plane) in 3 different regimes: r r. In each regime, find the fixed points, draw the flow arrows on the y-axis and indicate the stability of each fixed point. c. [8pts] Draw the bifurcation diagram. Use dashed lines for unstable fixed points and solid lines for the stable ones.