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Russia Yekaterinburg
Section Mathematics
Title Analysis of stochastic dynamics in discrete-time macroeconomic Kaldor model
Author(-s) Ryashko L.B.a, Sysolyatina A.A.a
Affiliations Ural Federal Universitya
Abstract The article deals with discrete Kaldor macroeconomic model under the random disturbances. It is shown that in the deterministic version of the model, there are different regimes of dynamics: equilibria, cycles, invariant curves, and chaos. A parametric description of the intervals of structural stability is given for these regimes and the corresponding bifurcations. Under the influence of stochastic perturbations around the deterministic attractors, the stationary probability distributions of random states are formed. To describe the dispersion of random states around equilibria and cycles, the stochastic sensitivity functions technique and the method of confidence ellipses are used. A dependence of the stochastic sensitivity of the system from parameters is studied. The phenomena generated by noise-induced transitions between coexisting attractors are discussed.
Keywords discrete Kaldor model, business cycles, random perturbations, stochastic sensitivity function, noise-induced transitions, confidence ellipses
UDC 517.925, 519.216
MSC 39A28, 93E03
DOI 10.20537/vm150107
Received 15 January 2015
Language Russian
Citation Ryashko L.B., Sysolyatina A.A. Analysis of stochastic dynamics in discrete-time macroeconomic Kaldor model, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 1, pp. 60-70.
  1. Kaldor N. A model of the trade cycle, The Economics Journal, 1940, vol. 50, no. 197, pp. 78-92.
  2. Kaldor N. A model of economic growth, The Economic Journal, 1957, vol. 67, no. 268, pp. 391-624.
  3. Chang W.W., Smyth D.J. The existence and persistence of cycles in a non-linear model: Kaldor's 1940 model reexamined, The Review Economics Studies, 1971, vol. 38, no. 1, pp. 37-44.
  4. Varian H.R. Catastrophe theory and the business cycle, Economic Inquiry, 1979, vol. 17, no. 1, pp. 14-28.
  5. Gabisch G., Lorenz H.-W. Business cycle theory: a survey of methods and concepts, Berlin: Springer-Verlag, 1989, 248 p.
  6. Bischi G.I., Dieci R., Rodano G., Saltari E. Multiple attractors and global bifurcations in a Kaldor-type business cycle mode, Journal of Evolutionary Economics, 2001, no. 11, pp. 527-554.
  7. Neimark Yu.I. , Landa P.S. Stokhasticheskie i khaoticheskie kolebaniya (Stochastic and chaotic oscillations), Moscow: Nauka, 1987, 424 p.
  8. Crutchfield J.P., Farmer J.D., Huberman B.A. Fluctuation and simple chaotic dynamics, Phys. Rep., 1982, vol. 92, no. 2, pp. 45-82.
  9. Lasota A., Mackey M.C. Chaos, fractals, and noise: stochastic aspects of dynamic, New York: Springer-Verlag, 1994, vol. 97, 474 p.
  10. Anikin V.M., Golubentsev A.F. Analiticheskie modeli determinirovannogo khaosa (Analytical models of deterministic chaos), Moscow: Fizmatlit, 2007, 328 p.
  11. Bashkirtseva I., Ryashko L., Tsvetkov I. Stochastic sensitivity equilibria and cycles of one-dimensional discrete mappings, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelinejn. Din., 2009, vol. 17, no. 6, pp. 74-85 (in Russian).
  12. Bashkirtseva I., Ryashko L., Tsvetkov I. Sensitivity analysis of stochastic equilibria and cycles for the discrete dynamic systems, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 2010, vol. 17, pp. 501-515.
  13. Sacker R. On invariant surfaces and bifurcation of periodic solutions of ordinary differential equations, Report IMM-NYU 333, New York University, 1964.
  14. Kuznetsov Yu.A. Elements of applied bifurcation theory, New York: Springer, 2004, vol. 112, 632 p.
  15. Bashkirtseva I., Ryashko L. Sensitivity analysis of stochastic attractors and noise-induced transitions for population model with Allee effect, Chaos, 2011, vol. 21, no. 21, pp. 047514.
  16. Bashkirtseva I., Ryashko L., Slepukhina E. Noise-induced oscillation bistability and transition to chaos in FitzHugh-Nagumo model, Fluctuation and Noise Letters, 2014, vol. 13, no. 1, pp. 1450004.
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