Simulate the predator-prey equations. a. p (t ) =  p (t ) −  p (t ) r (t ) r (t ) = − r (t ) +  p (t ) r (t ) hint: i used the values alp=0.04; gam=0.08; bet=0.002; del=0.0004. b. add controls u, v to the predator-prey equations. p (t ) =  p (t ) −  p (t ) r (t ) + u (t ) r(t)= −r(t)+ p(t)r(t)+v(t) the controls could be predator or prey animals added or subtracted from the population (at some rate). suppose, for example, suppose prey animals are added at a fixed rate over a fixed period u(t)=u00 t1tt2  0 elsewhere investigate the impact of this control on the evolution of the population. c. find if possible, feedback control laws that can move the non-trivial equilibrium from its uncontrolled value to a target value. d. use the simulator to check the stability of the new (controlled) equilibrium.