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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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/

[1] Agapova T. A., Seregina C. F., Makroekonomika, Delo i servis, M., 2004

[2] Arnold V. I., Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978

[3] Kondratev N. D., Osoboe mnenie, Nauka, M., 1993

[4] Kulikov A. N., “O gladkikh invariantnykh mnogoobraziyakh polugruppy nelineinykh operatorov v banakhovom prostranstve”, Issledovaniya po ustoichivosti i teorii kolebanii, ed. Kolesov Yu. S., YarGU, Yaroslavl, 1976, 114–129

[5] Kulikov A. N., Kulikov D. A., “Lokalnye bifurkatsii ploskikh beguschikh voln obobschennogo kubicheskogo uravneniya Shrëdingera”, Differ. uravn., 46:9 (2010), 1290–1299 | MR | Zbl

[6] Kulikov D. A., “Effekt zapazdyvaniya i ekonomicheskie tsikly”, Itogi nauki tekhn. Ser. Sovr. mat. prilozh. Temat. obz., 217 (2022), 41–50 | DOI | MR

[7] Lebedev V. V., Lebedev K. V., Matematicheskoe modelirovanie nestatsionarnykh protsessov, eTect, M., 2011

[8] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969

[9] Guckenheimer J., Holmes P. J., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 1983 | MR | Zbl

[10] Hale J., Theory of Functional Differential Equations, Springer-Verlag, Berlin, 1977 | MR | Zbl

[11] Marsden J. E., McCraken M., The Hopf Bifurcations and Its Applications, Springer, New York, 1976 | MR

[12] Puu T., Nonlinear Economic Dynamics, Springer-Verlag, Berlin, 1997 | MR | Zbl

[13] Radin M. A., Kulikov A. N., Kulikov D. A., “The influence of spatial effects on the dynamics of solutions in Keynes' mathematical model of the business cycle”, Nonlin. Dyn. Psychol. Life Sci., 26:4 (2022), 441–463 | MR

[14] Zhang W. B., Synergetic Economics: Time and Change in Nonlinear Economics, Springer-Verlag, Berlin, 1991 | MR | Zbl