Complex dynamics in the 1:3 spatial resonance

The interaction between two steady-state bifurcations with spatial wave numbers in the ratio 1:3 is considered. Periodic boundary conditions are assumed. The resulting O(2) equivariant normal form, truncated at third order, exhibits a number of global bifurcations that may result in complex dynamics. The origin of this behavior is elucidated with the help of careful numerical simulations and analysis of appropriate return maps. The results generalize to other 1:n resonances.