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Dynamics of the degenerate 2D Ricker equation
Author(s) -
Ryals Brian
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5360
Subject(s) - mathematics , degenerate energy levels , invariant (physics) , dynamics (music) , population , stability (learning theory) , mathematical analysis , conjugate , pure mathematics , mathematical physics , demography , physics , quantum mechanics , acoustics , machine learning , sociology , computer science
The dynamics of the 2D Ricker equation depend on the positioning of its isoclines. We give a complete description for the parameter values where the two isoclines overlap. In this case, we show the plane is covered by a family of invariant curves and that the restriction to each is conjugate to a family of one‐dimensional population maps. Properties of these 1D maps, including global stability, are established, and we discuss the implications for the 2D Ricker equation.