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.
Halloy
José
J
Service of Social Ecology, Université Libre de Bruxelles (U.L.B.), Boulevard du Triomphe, Campus de la Plaine, C.P. 231, Building NO, Brussels B-1050, Belgium. jhalloy@ulb.ac.be
Sonnino
Giorgio
G
Coullet
Pierre
P