9.6 Differential Equations
Predator & Prey Systems
Question #4 (Medium): Finding All Equilibrium Solutions to Prey-Predator System
Lotka-Volterra equations can be used to model population of horses and lions.
1) Given the equations, what happens to the horse population in the absence of lions?
2) Find all the equilibrium solutions and explain their significance.
3) The figure shows the phase trajectory that starts at the point . Describe what
eventually happens to the horse and lion populations.
4) Sketch graphs of the horse and lion populations as functions of time.
1) When lions are absent, then the lion variable , then ( ). For
( ), then , and . Since when ,
thus the horse population can be expected to increase up to for these values of H. When
, , then for these values of , the horse population is expected to decrease.