Problem 3. Dr. Dinamica is working in biomedical industry and is recently studying a model on the interaction between the glucose and the hormone in human body. The model has the following variables: G: the volume of glucose; H: the volume of hormone: . Go: the steady-state volume of glucose; Ho: the steady-state volume of hormone: g: the deviation of glucose from the steady-state volume, i.e., g = G-Go h: the deviation of hormone from the steady-state volume, i.e., h = H - H And the model reads the following linear dynamical system: = -mig-mgh; h = mag-mah; where mi: The average hormone-independent rate at which the system tends to return the blood glucose con- centration towards its steady-state value; m2: The lumped effect of the change of the liver set-point for glucose absorption or release, and of the change of the rate of glucose removal by the other tissues due to changes in h; m3: The glucose-independent rate at which the system tends to return the net hormone towards the steady-state volume: my: The lumped effects of the stimulation of the endocrine system by departures of glucose from its fasting values and possibly the protection of insulin from metabolic removal. are all parameters considered as constant. Based on the above information, answer the following questions: (1) Explain the meaning of (9,0) = (0,0) being a fixed point in this biomedical context. (2) What should be the sign of my, m2, m3, ma? Explain the reason (3) Now suppose that the coefficients matrix -mi-m2 mi --m3 has a pair of conjugate eigenvalues. For a person of normal physical condition, the fixed point should be which type? (Center? Nodal Source? Spiral sink? Or other type Specify it and explain the reason)