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The mathematical models of such processes are called differential systems with impulse effect.
Therefore mathematical models of such processes include an additional parameter which is called the control or disturbance vector depending on the character of the exterior influences.
As detailed models of such processes turn out to be very complicated, POD is an attractive way to obtain reduced models of low order.
The mechanisms underlying the fates of HSCs are still largely unknown, although several descriptive models of such processes have been established.
In classical models of such processes external or internal factors initiate and drive differentiation steps in a non-reversible manner.
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Increased interest in the technology motivated the development of accurate models of such process in recent years.
For realistic modeling of such processes these uncertainties have to be considered.
Mathematical modeling of such processes is essential to understand the entire mechanism.
The modeling of such processes requires comprehensive reaction schemes along with kinetic parameters to describe each of these mechanisms.
The modelling of such processes was firstly developed assuming perfect mixing for the whole system as a black box.
Therefore, modelling of such processes is a real problem which attracts special attention to the research of possible stable configurations and shapes of nanocrystals [30 36].
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