Dynamical bifurcations and competing instabilities in Landau and Landau-Ginzburg theory

We discuss the case of a Landau theory for systems with competing instabilities and the behavior of its solutions at the phase transition. We show that when one takes into account the finite speed of variation of control parameters in any real experiment, the jumping effects characteristic of dynamical bifurcation theory lead to an enhancement of the critical mode; we then apply our discussion to the Landau-Ginzburg equation. We corroborate our discussion by the results of numerical simulations.