For the predator–prey problem in Section 2.2, show by using Problem 2.25 that all solutions in  are periodic. 1. Show that the phase paths of the Hamiltonian system  are given byH(x,y)=constant....

For the predator–prey problem in Section 2.2, show by using Problem 2.25 that all solutions in
 are periodic.

1. Show that the phase paths of the Hamiltonian system
 are given byH(x,y)=constant. Equilibrium points occur at the stationary points of H(x,y).If(x0,y0)is an equilib-rium point, show that(x0,y0)is stable according to the linear approximation if H (x,y) has a maximum or a minimum at the point. (Assume that all the second derivatives of Hare nonzero at x₀,y₀)