Konstantin Shlufman
ul. Sholom-Aleikhem 4, Birobidzhan, 679016, Russia
Institute for Complex Analysis of Regional Problems, Far Eastern Branch of RAS
Publications:
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Shlufman K. V., Neverova G. P., Frisman E. Y.
Dynamic modes of the Ricker model with periodic Malthusian parameter
2017, Vol. 13, No. 3, pp. 363-380
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.
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Shlufman K. V., Neverova G. P., Frisman E. Y.
Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability
2016, Vol. 12, No. 4, pp. 553-565
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.
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