According to this, a short read.
When Nitrates become to low cyano reverts to acquiring its own Nitrate by dissolving N2 and uses light to carry the process further to ammonia. From there it converts to nitrate.
With this in mind to ellimenate cyano, a reduction in nitrates will cause the cyano to revert to producing its own nitrate for growth but it has to have a light source to carry this out, reducing nitrates and a black out period should do the trick.
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Cyanobacteria have a remarkable ability to store essential nutrients and metabolites
within their cytoplasm. Prominent cytoplasmic inclusions for this purpose can be seen
with the electron microscope (e.g. glycogen granules, lipid globules, cyanophycin
granules, polyphosphate bodies, carboxysomes) (Fay and Van Baalen, 1987). Reserve
products are accumulated under conditions of an excess supply of particular nutrients.
For example, when the synthesis of nitrogenous cell constituents is halted because of an
absence of a usable nitrogen source, the primary products of photosynthesis are
channelled towards the synthesis and accumulation of glycogen and lipids.
Dinitrogen fixation is a fundamental metabolic process of cyanobacteria, giving them the
simplest nutritional requirements of all living organisms. By using the enzyme
nitrogenase, they convert N2 directly into ammonium (NH4) (a form through which
nitrogen enters the food chain) and by using solar energy to drive their metabolic and
biosynthetic machinery, only N2, CO2, water and mineral elements are needed for growth
in the light. Nitrogen-fixing cyanobacteria are widespread among the filamentous,
heterocyst forming genera (e.g. Anabaena, Nostoc) (Stewart, 1973). However, there are
also several well documented examples of dinitrogen fixation among cyanobacteria not
forming heterocysts (e.g. Trichodesmium) (Carpenter et al., 1992). Under predominantly
nitrogen limited conditions, but when other nutrients are available, nitrogen fixing
cyanobacteria may be favoured and gain growth and reproductive success. Mass
developments (often referred to as "blooms") of such species in limnic (e.g. eutrophic
lakes, see Figure 2.2 in the colour plate section) and marine environments (e.g. the
Baltic Sea) are common phenomena world-wide.
Many species of cyanobacteria possess gas vesicles. These are cytoplasmic inclusions
that enable buoyancy regulation and are gas-filled, cylindrical structures. Their function
is to give planktonic species an ecologically important mechanism enabling them to
adjust their vertical position in the water column (Walsby, 1987). To optimise their
position, and thus to find a suitable niche for survival and growth, cyanobacteria use
different environmental stimuli (e.g. photic, gravitational, chemical, thermal) as clues.
Gas vesicles become more abundant when light is reduced and the growth rate slows
down. Increases in the turgor pressure of cells, as a result of the accumulation of
photosynthate, cause a decrease in existing gas vesicles and therefore a reduction in
buoyancy. Cyanobacteria can, by such buoyancy regulation, poise themselves within
vertical gradients of physical and chemical factors (Figures 2.3A and 2.3B). Other
ecologically significant mechanisms of movement shown by some cyanobacteria are
photomovement by slime secretion or surface undulations of cells (Häder, 1987; Paerl,
Complete article here
http://www.who.int/water_sanitation_health/resourcesquality/toxcyanchap2.pdf
I would also think if you have the ability to change the wave length of your light from yellow greens to blues it would keep them from regrowing. Cyano apparently has the ability to utilize all of the visible wave lengths but it has to go through an adaptation period to do so.