0
2013
Impact Factor

    Konstantin Shlufman

    ul. Sholom-Aleikhem 4, Birobidzhan, 679016, Russia
    Institute for Complex Analysis of Regional Problems, Far Eastern Branch of RAS

    Publications:

    Shlufman K. V., Neverova G. P., Frisman E. Y.
    Abstract
    The paper studies dynamic modes of the Ricker model with the periodic Malthusian parameter. The equation parametric space is shown to have multistability areas in which different dynamic modes are possible depending on the initial conditions. In particular, the model trajectory can asymptotically tend either to a stable cycle or to a chaotic attractor. Oscillation synchronization of the 2-cycles and the Malthusian parameter of the model are studied. Fluctuations in population size and environmental factors can be either synchronous or asynchronous. The structural features of attraction basins in phase space are investigated for possible stable dynamic modes.
    Keywords: recurrence equation, Ricker model, periodic Malthusian parameter, stability, bifurcation, dynamic modes, phase space, basins of attraction, multistability
    Citation: Shlufman K. V., Neverova G. P., Frisman E. Y.,  Dynamic modes of the Ricker model with periodic Malthusian parameter, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 3, pp.  363-380
    DOI:10.20537/nd1703005
    Shlufman K. V., Neverova G. P., Frisman E. Y.
    Abstract
    This paper investigates the emergence and stability of 2-cycles for the Ricker model with the 2-year periodic Malthusian parameter. It is shown that the stability loss of the trivial solution occurs through the transcritical bifurcation resulting in a stable 2-cycle. The subsequent tangent bifurcation leads to the appearance of two new 2-cycles: stable and unstable ones. As a result, there is multistability. It is shown that the coexistence of two different stable 2-cycles is possible in a narrow area of the parameter space. Further stability loss of the 2-cycles occurs according to the Feigenbaum scenario.
    Keywords: recurrence equation, Ricker model, periodic Malthusian parameter, stability, bifurcation, multistability
    Citation: Shlufman K. V., Neverova G. P., Frisman E. Y.,  Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 4, pp.  553-565
    DOI:10.20537/nd1604001

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