Multiple Bifurcations of Critical Period for a Quartic Kolmogorov Model

Our work is concerned with the bifurcation of critical period for a quartic Kolmogorov system.By computing the periodic constants carefully,we show that point(1,1)can be a weak center of fourth order,and the weak centers condition is given.Moreover,point(1,1)can bifurcate 4 critical periods under a certain condition.In terms of multiple bifurcation of critical periodic problem for Kolmogorov model,studied results are less seen,our work is good and interesting.