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.