A four dimensional allele selective migration model with three limit cycles
In this paper,we mainly studied the four-dimensional allelic selection transfer model.Ac-cording to Liapunov stability theorem,Hopf bifurcation theory,and central manifold theorem,two stable limit cycles are obtained by using Maple's program Liapunov constant to calculate the central focus quantity La,and it is concluded that the system belongs to the Zeeman class 27.Then an unsta-ble limit cycle is obtained according to Poincaré-Bendixson ring field theorem,and then it is deduced that there are three limit cycles in the four-dimensional allele selection transfer model.
limit cycleallelicselection transfer modelcenter manifold theorem
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