Geodesic
Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability
Russian journal of nonlinear dynamics, Tome 12 (2016) no. 4, pp. 553-565

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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, multistability.
Mots-clés : bifurcation 
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     author = {K. V. Shlufman and G. P. Neverova and E. Ya. Frisman},
     title = {Two-cycles of the {Ricker} model with the periodic {Malthusian} parameter: stability and multistability},
     journal = {Russian journal of nonlinear dynamics},
     pages = {553--565},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2016_12_4_a0/}
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K. V. Shlufman; G. P. Neverova; E. Ya. Frisman. Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability. Russian journal of nonlinear dynamics, Tome 12 (2016) no. 4, pp. 553-565. http://geodesic.mathdoc.fr/item/ND_2016_12_4_a0/