Bifurcation in Z2-symmetry quadratic polynomial systems with delay

Z2-symmetry systems are considered. Firstly the general forms of Z2-symmetry quadratic polynomial system are given, and then a three-dimensional Z2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.