3. 4 . Multiple Equilibria in Two Dimensions 147 predator per capita death rate is 0. 001 . If the prey population size is N and the predator population size is P. we have the differential equations N' = IN ( 1 - Fang ) P' = O. DOINP - O. ODIP. Find the equilibria of this system . 5000 ) - O. OINP . 3 . Using SageMath , plot the vector field of the predator-prey system described in Further Exercise 3. 4 . 2 and classify the equilibria . How do they differ from those in the Lotka - Volterra model ?13.4 . Multiple Equilibria in Two Dimensions 141 Exercise 3 . 4 . 2 Find the M- nullcline for the first deer-moose competition model , D' = D ( 3 - M - D ) , M' = M ( 2 - M - 0. 5D ). If we plot the nullclines D' = 0 and M' = O, we see the result in Figure 3. 22. You can see that vectors crossing the D- nullclines ( blue ) are vertical and those crossing the M- nullclines ( red ) are horizontal . Equilibrium points are the points at which nullclines cross . For example , an equilibrium at which the two species coexist exists only if the nullclines cross at a point away from the axes