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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 3, Pages 428–449
DOI: https://doi.org/10.31857/S0044466921030121 (Mi zvmmf11211) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Partial Differential Equations

Bifurcations of self-oscillatory solutions to a nonlinear parabolic equation with a rotating spatial argument and time delay

E. P. Kubishkin, V. A. Kulikov

P. G. Demidov Yaroslavl State University, Faculty of Mathematics
Citations (5)
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DOI: https://doi.org/10.31857/S0044466921030121
Abstract: For a problem arising in nonlinear optics, namely, for an initial-boundary value problem in a disk for a nonlinear parabolic equation with time delay and rotation of spatial argument by a given angle, bifurcations of self-oscillatory solutions from homogeneous equilibrium states are studied. In the plane of basic parameters of the equation, domains of stability (instability) of homogeneous equilibrium states are constructed, and the dynamics of the stability domains is analyzed depending on the delay value. The mechanisms of stability loss of homogeneous equilibrium states are investigated, possible bifurcations of spatially inhomogeneous self-oscillatory solutions and their stability are analyzed, and the dynamics of such solutions near the boundary of a stability domain in the plane of basic parameters of the equation is studied.
Key words: delay differential equation, spatially inhomogeneous solutions, bifurcation of multistability.
Funding agency Grant number
Russian Foundation for Basic Research 19-31-90133
This work was supported by the Russian Foundation for Basic Research, project no. 19-31-90133.
Received: 13.02.2020
Revised: 26.09.2020
Accepted: 18.11.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 3, Pages 403–423
DOI: https://doi.org/10.1134/S0965542521030118
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: E. P. Kubishkin, V. A. Kulikov, “Bifurcations of self-oscillatory solutions to a nonlinear parabolic equation with a rotating spatial argument and time delay”, Zh. Vychisl. Mat. Mat. Fiz., 61:3 (2021), 428–449; Comput. Math. Math. Phys., 61:3 (2021), 403–423
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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