Finding a Ljapunov function for discrete dynamical system with 3 variables.

Question

Consider the discrete dynamical system given by $(x_{k+1},y_{k+1},z_{k+1}) = f(x_k,y_k,z_k)$, where $f(x,y,z) = (x(1-ay),y(1-b+ax),z+by)$ with $a,b \in (0,1)$ are parameter and we are only interested in $x,y,z \in [0,1]$ with $x+y+z=1$. The set of all fixed points is given by all $(x,0,z) \in [0,1]^3$ with $x+z=1$. Now, the Jacobi matrix of $f$ at such a point has $1$ as eigenvalue and so we cannot make assertions about stability with the usual criterion. How do we find a Ljapunov function for these fixed points?