Nonlinear dynamics of subcritical instabilities in the presence of a
feedback control is investigated. The control is based on a feedback loop
between the linear growth rate and the maximum of the amplitude of the
emerging pattern.
In the case of a subcritical monotonic instability, the globally
controlled Sivashinsky equation is considered. It is shown that the global
control can prevent the blowup, and spatially localized structures are
formed. The subcritical oscillatory instability is studied in the
framework of a globally controlled complex GinzburgLandau equation. In
the latter case, the global control results in formation of spatially
localized pulses. In the onedimensional case, depending on the values of
the linear and nonlinear dispersion coefficients, several types of the
pulse dynamics are possible in which the computational domain contains:
(i) a single stationary pulse; (ii) several coexisting stationary pulses;
(iii) competing pulses that appear one after another at random locations
so that at each moment of time there is only one pulse in the domain; (iv)
temporal intermittency between cases (ii) and (iii); (v) spatiotemporally
chaotic system of short pulses. In the twodimensional case, alternating
or chaotic pulses are found.
