Geodesic
The influence of competition on the dynamics of macroeconomic systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 2, Tome 228 (2023), pp. 20-31.

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The problem of interaction (competition) of two identical macroeconomic systems is studied in the case where the dynamics of each of them is modeled by the well-known Keynes system of differential equations. It is shown that this problem can be interpreted as the problem of synchronization of two self-oscillating systems. The analysis is based on the method of integral manifolds and Poincaré method of normal forms. We prove that three types of oscillations arise in the problem: completely synchronous self-oscillations, antiphase oscillations, and asymmetric oscillations. For all solutions, their stability is examined and asymptotic formulas are obtained.
Keywords: Keynes model, economic cycle, competition, integral manifold, asymptotics, normal form, stability
Mots-clés : bifurcation 
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A. N. Kulikov; D. A. Kulikov; D. G. Frolov. The influence of competition on the dynamics of macroeconomic systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 2, Tome 228 (2023), pp. 20-31. http://geodesic.mathdoc.fr/item/INTO_2023_228_a2/

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