Bonus (+6): Determine the bifurcation value(s) for the one-parameter family of DES (with parameter a). Show work. dy dt + ay +4 Bifurcation value(s): Draw a representative phase line for DEs in each category listed below, along with a representative solution curve for each interval between critical points. For each, include labeled equilibrium points (if any), arrows on the phase line, representative curves, and identify each equilibrium as stable, unstable, or semi-stable. 1. a=0 (if this is different from the largest bifurcation value) 2. a equal to the largest bifurcation value (if there is more than one) 3. a one unit larger than the largest bifurcation value Sketch a bifurcation diagram representing the phase portraits of this family of DEs as the value of the parameter a is varied. You many need to consider more representative phase lines than those above. Bonus (+6): Determine the bifurcation value(s) for the one-parameter family of DES (with parameter a). Show work. dy dt + ay +4 Bifurcation value(s): Draw a representative phase line for DEs in each category listed below, along with a representative solution curve for each interval between critical points. For each, include labeled equilibrium points (if any), arrows on the phase line, representative curves, and identify each equilibrium as stable, unstable, or semi-stable. 1. a=0 (if this is different from the largest bifurcation value) 2. a equal to the largest bifurcation value (if there is more than one) 3. a one unit larger than the largest bifurcation value Sketch a bifurcation diagram representing the phase portraits of this family of DEs as the value of the parameter a is varied. You many need to consider more representative phase lines than those above