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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2024 Volume 237, Pages 18–33 (Mi into1322)

Local bifurcations in one version of the multiplier-accelerator model

A. N. Kulikov, D. A. Kulikov, D. G. Frolov

P.G. Demidov Yaroslavl State University

Abstract: The well-known mathematical model of macroeconomics “multiplier-accelerator” is considered in a nonlinear version with spatial factors. We study two versions of the corresponding boundary-value problem. In the first version, where the spatial dissipation is significant in the linear statement, the boundary-value problem has limit cycles that arise as a result of Andronov–Hopf bifurcations. The second version of the boundary-value problem arises when dissipation in the linear formulation is neglected. In this weakly dissipative version, the boundary-value problem has a countable set of finite-dimensional cycles and tori. All such invariant manifolds are unstable. The analysis of the problem is based on methods of the theory of infinite-dimensional dynamic systems.

Keywords: multiplier-accelerator, nonlinear boundary value problem, invariant manifold, bifurcation, stability, normal form

UDC: 517.929

MSC: 35L10, 35L30, 37N40

DOI: 10.36535/2782-4438-2024-237-18-33



© Steklov Math. Inst. of RAS, 2025