Economic and mathematical models for analysis of complex systems in the economy based on generalized Samuelson-Hicks equations

Kh.Kh. Kalazhokov , F.Kh. Uvizheva

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Abstract: The work is devoted to the issues of construction, implementation, as well as the application of economic and mathematical models for the study of processes in the regional economy. The possibilities of a long-term analysis of the regional economy within the framework of the Samuelson-Hicks model using a two-point boundary value problem, the point of which is to solve the boundary value problem by the method of twice solving the Cauchy problem in combination with the sweep method, are presented. The method of invariant immersion is proposed to improve the efficiency of the analysis of regional economies, the point of which is to solve two-point boundary value problems by reducing them to the system of Cauchy problems. The length of the time interval of the solving problem is the immersion parameter in constructing solutions to systems of Cauchy problems.

Keywords: macroeconomics, generalized equations, two-point boundary value problem, invariant immersion method, differential process immersion method, Samuelson-Hicks model

For citation. Kalazhokov Kh.Kh., Uvizheva F.Kh. Economic and mathematical models for analysis of complex systems in the economy based on generalized Samuelson-Hicks equations. News of the Kabardino-Balkarian Scientific Center of RAS. 2023. No. 1(111). Pp. 48–56. DOI: 10.35330/1991-6639-2023-1-111-48-56

References

1. Berezin I.S., Zhidkov N.P. Metody vychislenij [Calculation methods]. Moscow: Izdatel’stvo fiziko-matematicheskoj literatury, 1962. Vol. 2. 464 p. (In Russian)
2. Kasta Dzh., Kalaba R. Metody pogruzheniya v prikladnoj matematike [Immersion methods in applied mathematics]. Moscow: Mir, 1976. (In Russian)
3. Tramontana F., Gardini L. Revisiting Samuelson’s models, linear and nonlinear, stability conditions and oscillating dynamics. Economic Structures. 2021. No. 10. Art. 9. https://doi.org/10.1186/s40008-021-00239-3
4. Barros M.F., Ortega F. An optimal equilibrium for a reformulated Samuelson economic discrete time system. Economic Structures. 2019. No. 8. Art. 29. https://doi.org/10.1186/s40008-019-0162-2
5. Ortega F., Barros M.F. The Samuelson macroeconomic model as a singular linear matrix difference equation. Economic Structures. No. 9. Art. 36. https://doi.org/10.1186/s40008-020-00207-3
6. Kalazhokov Kh.Kh., Uvizheva F.Kh. The study of non-equilibrium processes in the monetary economy by immersion in the differential process. News of the Kabardino-Balkarian Scientific Center of RAS. 2020. No. 1(93). Pp. 35–45. DOI: 10.35330/1991-6639-2020-1-93-35-45. (In Russian)

Information about the authors

Kalazhokov Khasan Khazhmurzovich, Senior Staff Scientist of the Department of Mathematical Methods of Research of Complex Systems and Processes, Institute of Computer Science and Problems of Regional Management – branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
360000, Russia, Nalchik, 37-a I. Armand street;
khasan_kalazhokov@mail.ru, ORCID: https://orcid.org/0000-0002-7523-9353
Uvizheva Fatima Khasanovna, Staff Scientist of the Department of Mathematical Methods of Research of Complex Systems and Processes, Institute of Computer Science and Problems of Regional Management – branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
360000, Russia, Nalchik, 37-a I. Armand street;
fatimauvizheva@mail.ru, ORCID: https://orcid.org/0000-0001-8228-8543