The LotkaVolterra preypredator system with self-limitation of prey is given by 5% = rm) = w cw as, g = am) = y(s +622) where a, b, c, r and s are positive constants. (i) Find the three steady states of the system and determine (where relevant) conditions for them to be biologically realistic (i.e. populations are non-negative). (ii) Determine whether the three steady states are stable or unstable (you do not need to show whether they are nodes/spirals/saddles), and show in particular that the co-existence steady state (x*, y*) is stable whenever it is biologically realistic. (iii) Sketch the phase plane in the case that (33*, y*) is biologically realistic, marking the steady states, the nullclines, the direction eld on the nullclines and in the regions between them. Note that the nullcline f = 0 given by r ca: my = 0 is not a horizontal line. (iv) Sketch a solution trajectory that illustrates the stability of (02*, y*). (v) In the case that (:c\