Geodesic
The influence of delay and spatial factors on the dynamics of solutions in the mathematical model ``supply-demand''
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 1, Tome 230 (2023), pp. 75-87

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A generalized version of the macroeconomic model “supply-demand” is considered. The main version of this model possesses a single attractor, namely, the state of economic equilibrium. We analyze a nonlinear boundary-value problem for a partial differential equation with delay on the right-hand side. The analysis of solutions in a neighborhood of the equilibrium state is reduced to the study of local bifurcations of the complex Ginzburg–Landau equation. For the basic boundary-value problem, the existence of cycles is proved, including cycles depending on the spatial variable.
Keywords: mathematical model «supply-demand», boundary-value problem, Ginzburg–Landau equation, stability, cycle, asymptotics
Mots-clés : bifurcation 
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     author = {A. N. Kulikov and D. A. Kulikov},
     title = {The influence of delay and spatial factors on the dynamics of solutions in the mathematical model ``supply-demand''},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {75--87},
     publisher = {mathdoc},
     volume = {230},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_230_a6/}
}
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A. N. Kulikov; D. A. Kulikov. The influence of delay and spatial factors on the dynamics of solutions in the mathematical model ``supply-demand''. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 1, Tome 230 (2023), pp. 75-87. http://geodesic.mathdoc.fr/item/INTO_2023_230_a6/