We consider a predator-prey system of Leslie type with generalized Holling type III functional response p(x) = mx(2)/ax(2)+bx+1. By allowing b to be negative (b > -2 root a), p(x) is monotonic for b > 0 and nonmonotonic for b < 0 when x >= 0. The model has two non-hyperbolic positive equilibria (one is a multiple focus of multiplicity one and the other is a cusp of codimension 2) for some values of parameters and a degenerate Bogdanov-Takens singularity (focus or center case) of codimension 3 for other values of parameters. When there exist a multiple focus of multiplicity one and a cusp of co...
