Asymptomatic and limiting behavior of dynamic system of double hypercycle

M.V. Safro

Asymptomatic and limiting behavior of dynamic system of double hypercycle

M.V. Safro¹

research article Pages: 172-179

¹ аспирант, МГУПС (МИИТ)

Keywords: double hypercycle ecological stability permanence variability

Abstract

In the real work the model of hyper cyclic replication at which each macromolecule catalyzes emergence of two subsequent macromolecules in the closed cycle is studied. It is proved that such system possesses property of not degeneracy (permanence). Stability of stationary positions of balance is studied.

How to cite

Сафро М.В. Асимптотика и предельное поведение динамической системы двойного гиперцикла // Нелинейный мир. 2013. № 3. С. 172–179.

References

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[1] Arnold V.I. Dopolnitelnye glavy teorii obyknovennykh differencialnykh uravnenijj. M.: Nauka. 1978.

[2] Bratus A.S., Novozhilov A.S., Platonov A.P. Dinamicheskie sistemy i modeli biologii. M.: Fizmatlit, 2010.

[3] Hofbauer J., Sigmund K. Evolutionary Games and Population Dynamics. Cambridge: Cambridge University Press. 1998.

[4] Bellman R. Vvedenie v teoriju matric. M.: Nauka. 1969.

[5] Hofbauer J., Mallet-Paret J., Smith H. L. Stable periodic solutions for the hypercycle system // Journal of Dynamics and Differential Equations. 1991. V. 3.

[6] Mallet-Paret J., Smith H. L. The Poincare-Bendixson theorem for monotone cyclic feedback systems // Journal of Dynamics and Differential Equations. 1990. V. 2. R. 367-421.