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## Archive of Issues

Russia Yekaterinburg
Year
2018
Volume
28
Issue
1
Pages
3-14
 Section Mathematics Title The phenomenon of stochastic excitability in the enzymatic reaction model Author(-s) Bashkirtseva I.A.a, Zaitseva S.S.a Affiliations Ural Federal Universitya Abstract We study the influence of noise on the Goldbeter model of the enzymatic reaction, which describes the mechanism of oscillatory synthesis of cyclic adenosine monophosphate in a cell. It is shown that the model is highly sensitive to variations of parameters and initial conditions. The phenomenon of stochastic excitability in a stable equilibrium zone is demonstrated and studied. We show that the noise results in a sharp transition from low-amplitude stochastic oscillations to large-amplitude spike oscillations. For the parametric analysis of this phenomenon, the technique of stochastic sensitivity functions and the method of confidence ellipses are used. We study how the critical value of the noise intensity corresponding to the generation of large-amplitude oscillations depends on the proximity of a control parameter to a bifurcation point. For a detailed analysis of the frequency properties of stochastic oscillations, a statistical analysis of interspike intervals is carried out, and a phenomenon of coherent resonance is found. Keywords random disturbances, excitability, stochastic sensitivity, confidence ellipses UDC 517.977 MSC 93E03 DOI 10.20537/vm180101 Received 25 December 2017 Language Russian Citation Bashkirtseva I.A., Zaitseva S.S. The phenomenon of stochastic excitability in the enzymatic reaction model, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 1, pp. 3-14. References Horsthemke W., Lefever R. Noise-induced transitions, Berlin: Springer, 1984, 322 p. Anishchenko V.S., Astakhov V.V., Vadivasova T.E., Neiman A.B., Strelkova G.I., Shimanskii-Gaier L. 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