We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class...We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class of rational differential systems with a cubic polynomial as its numerator.展开更多
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 cent...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.展开更多
基金supported by the National Natural Science Foundation of China (10961011)the Slovene Human Resources and Scholarship Fundthe Slovenian Research Agency, by the Nova Kreditna Banka Maribor, by TELEKOM Slovenije and by the Transnational Access Programme at RISC-Linz of the European Commission Framework 6 Programme for Integrated Infrastructures Initiatives under the project SCIEnce (Contract No. 026133)
文摘We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class of rational differential systems with a cubic polynomial as its numerator.
基金This paper is supported by National Natural Science Foundation of China(12061016)the Research Fund of Hunan provincial education department(18A525)the Hunan provincial Natural Science Foundation of China(2020JJ4630)。
文摘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.
