Hopf bifurcation in symmetric configuration of predator–prey-mutualist systems

In this paper we apply the equivariant degree method to study Hopf bifurcations in a system of differential equations describing a symmetric predator–prey-mutualist model with diffusive migration between interacting communities. A topological classification (according to symmetry types), of symmetric Hopf bifurcation in configurations of populations with D8, D12, A4 and S4 symmetries, is presented with estimation on minimal number of bifurcating branches of periodic solutions.