Geodesic
Local bifurcations in one version of the multiplier-accelerator model
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—XXXV", Voronezh, April 26-30, 2024, Part 3, Tome 237 (2024), pp. 18-33

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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, stability, normal form
Mots-clés : bifurcation 
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     title = {Local bifurcations in one version of the multiplier-accelerator model},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     volume = {237},
     year = {2024},
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A. N. Kulikov; D. A. Kulikov; D. G. Frolov. Local bifurcations in one version of the multiplier-accelerator model. 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—XXXV", Voronezh, April 26-30, 2024, Part 3, Tome 237 (2024), pp. 18-33. http://geodesic.mathdoc.fr/item/INTO_2024_237_a2/