$x^{\text{'}}(t)=-xz,z^{\text{'}}(t)=x-z.$

since $y=1-x.$ This system has a unique equilibrium point when $x=z=0,$ that is$,(0,0).$

Figures $(1)$ and $(2)$ Describe figure $(1)$ and $(2)$ given the two system of equations where x is the susceptible trees and z is the beetle population.