Geodesic
On one approach to modeling of living system regulatory mechanisms
Matematičeskoe modelirovanie, Tome 16 (2004) no. 7, pp. 77-91

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Some questions of quantitative analysis of living cell's regulatory system functioning based on the functional-differential equations are considered. Condition equations are constructed taking into account processes cooperation, presence of multifunction feedback and temporary relations in cellular regulatory system. Results of qualitative studies for the equations and their model systems show existence following modes: rest (A), stable functional condition (B), periodic (C) and irregular fluctuations (D). In some cases, there is the «black hole» effect (E) – failure of oscillatory solutions into stable trivial attractor. Correspondence possibility, during model studies, A, B, C, D, and E to real modes of rest, stationary state, stable fluctuations, unpredictable behavior and sudden activity stop allows using the proposed approach for quantitative studies of biosystems regulatory mechanisms at the norm and anomalies. 
@article{MM_2004_16_7_a8,
     author = {B. N. Hidirov},
     title = {On one approach to modeling of living system regulatory mechanisms},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {77--91},
     publisher = {mathdoc},
     volume = {16},
     number = {7},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_7_a8/}
}
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B. N. Hidirov. On one approach to modeling of living system regulatory mechanisms. Matematičeskoe modelirovanie, Tome 16 (2004) no. 7, pp. 77-91. http://geodesic.mathdoc.fr/item/MM_2004_16_7_a8/