Pattern formation in forced reaction diffusion systems with nearly degenerate bifurcations

The existence and stability of stable standing-wave patterns in an assembly of spatially distributed generic oscillators governed by a couple of complex Ginzburg-Landau equations, subjected to parametric forcing, are reported. The mechanism of a dispersion-induced pattern in dissipative oscillators parametrically forced near the degenerate Turing-Hopf bifurcation is also illustrated. We show that, when excitation occurs just after the Turing bifurcation and before the Hopf instability, the system exhibits a new type of stable standing-wave structures, namely the mixed-mode solutions. The Brussellator-model, parametrically forced below the threshold of oscillations, is analyzed as an example of calculation.