Geodesic
Modeling nonbranching multistage synthesis by an equation with retarded argument
Sibirskij žurnal industrialʹnoj matematiki, Tome 7 (2004) no. 1, pp. 73-94.

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We present the results of investigating a mathematical model of the nonbranching multistage synthesis of a substance. We show that in the passage to the limit in which the model has infinitely many stages we obtain an equation with retarded argument. We describe the properties of the solutions of the finite-dimensional model and of the equation with retarded argument. 
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V. A. Likhoshvai; S. I. Fadeev; G. V. Demidenko; Yu. G. Matushkin. Modeling nonbranching multistage synthesis by an equation with retarded argument. Sibirskij žurnal industrialʹnoj matematiki, Tome 7 (2004) no. 1, pp. 73-94. http://geodesic.mathdoc.fr/item/SJIM_2004_7_1_a7/

[1] Godunov S. K., Obyknovennye differentsialnye uravneniya s postoyannymi koeffitsientami T. 1. Kraevye zadachi, Ucheb. posobie, Izd-vo Novosib. gos. un-ta, Novosibirsk, 1994 | MR | Zbl

[2] Likhoshvai V. A., Matushkin Yu. G., Fadeev S. I., “Zadachi teorii funktsionirovaniya gennykh setei”, Sib. zhurn. industr. matematiki, 6:2(14) (2003), 64–80 | MR | Zbl

[3] Golubyatnikov V. P., Likhoshvai V. A., “Odnomernaya model razvitiya populyatsii zemnovodnykh”, Sib. zhurn. industr. matematiki, 5:2(10) (2002), 53–60 | MR | Zbl

[4] Kolchanov N. A., Ananko E. A., Kolpakov F. A., Podkolodnaya O. V., Ignateva E. V., Goryachkovskaya T. N., Stepanenko I. L., “Gennye seti”, Mol. biologiya, 34:4 (2000), 449–460

[5] Kolchanov N. A., “Regulyatsiya transkriptsii genov eukariot: bazy dannykh i kompyuternyi analiz”, Mol. biologiya, 31:4 (1997), 581–583

[6] Edwards R., Glass L., “Combinatorial explosion in model gene networks”, CHAOS, 2000, no. 10, 691–704 | DOI | MR | Zbl

[7] Elowitz M. B., Leibler S., “A synthetic oscillatory network of transcriptional regulators”, Nature, 2000, no. 403, 335–338 | DOI

[8] Gardner T. S., Cantor C. R., Collins J. J., “Construction of a genetic toggle switch in Escherichia coli”, Nature, 2000, no. 403, 339–342

[9] Thomas R., Thieffry D., Kaufman M., “Dynamycal behavior of biological regulatory networks-I. Biological role of feedback loops and practical use of the concept of the loopcharacteristic state”, Bull. Math. Biology, 1995, no. 57, 247–276 | Zbl

[10] Bazhan S. I., Likhoshvay V. A., Belova O. E., “Theoretical analysis of the regulation of interferon expression during priming and blocking”, J. Theor. Biol., 1995, no. 175, 149–160 | DOI

[11] Belova O. E., Likhoshvai V. A., Bazhan S. I., Kulichkov V. A., “Computer system for investigation and integrated description of molecular-genetic system regulation of interferon induction and action”, CABIOS, 11:2 (1995), 213–218

[12] Likhoshvai V. A., Matushkin Yu. G., Vatolin Yu. N., Bazhan S. I., “A generalized chamical kinetic metod for simulating complex biological systems. A computer model of $\lambda$-phage ontogenesis”, Comput. Technologies, 5:2 (2000), 87–99 | MR