The standard Lotka-Volterra predator-prey model is given below in nondimensional form. du/dt = u(1 â v) dv/dt = av(u â 1) A) Begin with the predator-prey model we derived in class, and non-dimensionalize it to obtain the above system. Explain what each term in the model equations represents. B) Use pplane to construct a phase portrait for the Lotka-Volterra system. Let a = 0.5 fixed, and show trajectories for several different initial conditions. C) Interpret your results in terms of the biology. What do you notice about the type and stability of fixed points (focus on the first quadrant since that is the only one with physical meaning)? D) ) Now investigate the effect that changing a has on the period of the predator and prey oscillations. i. Graph the predator and prey populations versus time for a = 0.5, 1, and 5. Use the initial condition (uo, vo) = (1, 2.5). ii. Estimate the period of the oscillations for each value of a.