Limit cycles of a cubic Kolmogorov system
The authors consider limit cycles which bifurcate from a critical point in case of cubic Kolmogorov systems of the form \[ \dot x=x(x-2y+2)(Ax+y+B),\quad \dot y=y(2x-y-2)(Dx+y+C).\tag{1} \] The authors use the computer algebra procedure FINDETA which was described by the first two authors [J. Symb. Comput. 9, No. 2, 215-224 (1990; Zbl 0702.68072)] to compute the focal values at the critical point \((2,2)\) and show that for certain cubic Kolmogorov systems (1), four and not more than four limit cycles can bifurcate from a critical point in the first quadrant; moreover, three fine foci of order one can coexist and a limit cycle can bifurcate from each.
scientific article; zbMATH DE number 915050