a) (15 pts) In the human body, the level of insulin can aect the way proteins interact. An increase in the amount of certain protein A increases the production of certain other protein B, while an increase in the amount of protein B decreases the production of protein A. When insulin levels are low, the amounts of proteins A and B stay at equilibrium, but when insulin levels are high, the amounts of A and B will oscillate. Give two reasons why the increase in insulin could cause these oscillations. Please note that your answer does not need to, and in fact should not, use any facts about the biology of insulin. (In other words, just use the assumptions above and what you have learned in this COurse.) b) (12 pts) Sketch the state space of a 2dimensional model with an unstable limit cycle surrounded by a stable limit cycle (and with no other limit cycles). Make sure to include some representa tive trajectories and any equilibrium point(s) the model must have. Label the limit cycles and equilibrium points with their types. Which of the objects in this diagram are attractors