Spectral Properties of the "Reaction-Diffusion" System Operators and Bifurcations Signs
- 作者: Yumagulov M.G.1, Vasenina N.A.1
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隶属关系:
- Ufa University of Science and Technology
- 期: 编号 2 (65) (2024)
- 页面: 17-25
- 栏目: Mathematics
- URL: https://journal-vniispk.ru/1993-0550/article/view/307272
- DOI: https://doi.org/10.17072/1993-0550-2024-2-17-25
- ID: 307272
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详细
The article discusses differential equations that arise when modeling reaction-diffusion systems. Questions about the stability of equilibrium points in critical cases, as well as about bifurcations in the vicinity of such points, are studied. The main attention is paid to the linearized problem operators spectral properties study. The spectrum discreteness was established, the root properties and invariant subspaces were studied, and formulas for eigenfunctions were proposed. As an application, questions about the multiple equilibrium bifurcation signs and Andronov –Hopf bifurcation in the vicinity of equilibrium points are discussed. Examples are given to illustrate the proposed approaches effectiveness in studying stability and bifurcations problems.
作者简介
M. Yumagulov
Ufa University of Science and Technology
编辑信件的主要联系方式.
Email: yum_mg@mail.ru
Doctor of Physical and Mathematical Sciences, Professor 32, Zaki Validi St., Ufa, Republic of Bashkortostan, Russia, 450076
N. Vasenina
Ufa University of Science and Technology
Email: zhiber.na@gmail.com
Candidate of Physical and Mathematical Sciences, Docent 32, Zaki Validi St., Ufa, Republic of Bashkortostan, Russia, 450076
参考
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