The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2...The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.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
The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated.The evolution equation related ...The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated.The evolution equation related to the Bogoliubov weights happens to be a solvable Mathieu equation when the coupling strength is periodically modulated.An exact relation between the time derivatives of momentum distribution and dynamical structure factor is derived,which indicates that the single-particle property is strongly related to the two-body property in the evolutions of Bose–Einstein condensates.It is found that the momentum distribution and dynamical structure factor cannot display periodical behavior.For stable dynamics,some particular peaks in the curves of momentum distribution and dynamical structure factor appear synchronously,which is consistent with the derivative relation.展开更多
The authors study the existence of almost periodic solutions to differential equations with piecewise constant arguments which found applications in certain biomedical problems.
This paper considers the problems of determining center or focus and isochronous centers for the planar quasi-analytic systems. Two recursive formulas to determine the focal values and period constants are given. The ...This paper considers the problems of determining center or focus and isochronous centers for the planar quasi-analytic systems. Two recursive formulas to determine the focal values and period constants are given. The convergence of first integral near the center is proved. Using the general results to quasi-quadratic systems, the problem of the isochronous center of the origin is completely solved.展开更多
In this paper, the definition of generalized isochronous center is given in order to study unitedly real isochronous center and linearizability of polynomial differential systems. An algorithm to compute generalized p...In this paper, the definition of generalized isochronous center is given in order to study unitedly real isochronous center and linearizability of polynomial differential systems. An algorithm to compute generalized period constants is obtained, which is a good method to find the necessary conditions of generalized isochronous center for any rational resonance ratio. Its two linear recursive formulas are symbolic and easy to realize with computer algebraic system. The function of time-angle difference is introduced to prove the sufficient conditions. As the application, a class of real cubic Kolmogorov system is investigated and the generalized isochronous center conditions of the origin are obtained.展开更多
文摘The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.
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.
基金financial support from the National Natural Science Foundation of China(Grants No.11675017 and No.11975050)。
文摘The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated.The evolution equation related to the Bogoliubov weights happens to be a solvable Mathieu equation when the coupling strength is periodically modulated.An exact relation between the time derivatives of momentum distribution and dynamical structure factor is derived,which indicates that the single-particle property is strongly related to the two-body property in the evolutions of Bose–Einstein condensates.It is found that the momentum distribution and dynamical structure factor cannot display periodical behavior.For stable dynamics,some particular peaks in the curves of momentum distribution and dynamical structure factor appear synchronously,which is consistent with the derivative relation.
文摘The authors study the existence of almost periodic solutions to differential equations with piecewise constant arguments which found applications in certain biomedical problems.
基金the National Natural Science Foundation of China (10671179 and 10771196)the Natural Science Foundation of Yunnan Province (2005A0092M)
文摘This paper considers the problems of determining center or focus and isochronous centers for the planar quasi-analytic systems. Two recursive formulas to determine the focal values and period constants are given. The convergence of first integral near the center is proved. Using the general results to quasi-quadratic systems, the problem of the isochronous center of the origin is completely solved.
基金Supported by Science Foundation of Hubei Province Education Department Q20091209National Natural Science Foundation of China (Grant No. 10871206)
文摘In this paper, the definition of generalized isochronous center is given in order to study unitedly real isochronous center and linearizability of polynomial differential systems. An algorithm to compute generalized period constants is obtained, which is a good method to find the necessary conditions of generalized isochronous center for any rational resonance ratio. Its two linear recursive formulas are symbolic and easy to realize with computer algebraic system. The function of time-angle difference is introduced to prove the sufficient conditions. As the application, a class of real cubic Kolmogorov system is investigated and the generalized isochronous center conditions of the origin are obtained.
