The following interactions define how substances u and v interact over time: uu+vv​→v/u2u,→12v→u/v∅.​ (i) Use the Law of Mass Action to show that the two ordinary differential equations that define the evolution of (u,v), assuming initial conditions u(0)= u0​ and v(0)=v0​, are dtdu​=v(1−u),dtdv​=u(v−1).​ (ii) Determine the two steady states. (iii) Derive the Jacobian of the system and characterise the linear stability of all steady states. (iv) Draw the (u,v) phase plane. Include and label: (a) nullclines; (b) directional arrows one each nullcline;