In this paper,the existence of nonconstant oscillating periodic solution of differential difference e-quation with n time lags is stutied:x′(t)=-g(x(t))[f(x(t-τ1))+f(x(t-τ2))+…+f(x(t-τn))] the results of Paper[1-...In this paper,the existence of nonconstant oscillating periodic solution of differential difference e-quation with n time lags is stutied:x′(t)=-g(x(t))[f(x(t-τ1))+f(x(t-τ2))+…+f(x(t-τn))] the results of Paper[1-6] are extended and improved.展开更多
Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if the rightmost characteristic root has negative real part. Based on the Lambert W...Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if the rightmost characteristic root has negative real part. Based on the Lambert W function, this paper presents a simple algorithm for locating the rightmost characteristic root of periodic solutions of some nonlinear oscillators with large time delay. As application, the proposed algorithm is used to study the primary resonance and 1/3 subharmonic resonance of the Duffing oscillator under harmonic excitation and delayed feedback, as well as the control problem of the van der Pol oscillator under harmonic excitation by using delayed feedback, with a number of case studies. The main advantage of this algorithm is that though very simple in implementation, it works effectively with high accuracy even if the delay is large.展开更多
In this work,the ionospheric variability is analyzed by applying the wavelet decomposition technique to the noontime fo F2,F10.7,interplanetary magnetic field(IMF)Bz,Ap,and lower thermospheric temperature at pressure ...In this work,the ionospheric variability is analyzed by applying the wavelet decomposition technique to the noontime fo F2,F10.7,interplanetary magnetic field(IMF)Bz,Ap,and lower thermospheric temperature at pressure of 10?4 h Pa in 2002.Results show that the variance of periodic oscillations in the ionosphere is largest in the 2–4-day period and declines with the increase of the period.The maximum variance of the periodic oscillations in solar irradiation is in the 16–32-day period.For geomagnetic activities,most of the variance is about equally distributed on intervals of periods shorter than 32 days.Variance distributions of IMF Bz and lower thermospheric temperature are similar to those of the ionosphere.They show the maximum in the 2–4-day period and decline with the increase of the period.By analyzing the distributions of the variances,the potential connections between the ionosphere and the external sources are discussed.展开更多
By using some analytical techniques, modified inequalities and Mawhin＇s continuous theorem of coincidence degree theory, some simple sufficient conditions for the existence of at least one positive almost periodic so...By using some analytical techniques, modified inequalities and Mawhin＇s continuous theorem of coincidence degree theory, some simple sufficient conditions for the existence of at least one positive almost periodic solution of a generalized Mackey-Glass model of respiratory dynamics are obtained. Further, the globM attractivity of positive almost periodic solution of the above model is also studied. To the best of the author＇s knowl- edge, so far, the result of this paper is completely new. Finally, three examples are given to illustrate the main results in this paper.展开更多
In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g a...In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g and e are regular, described precisely in the introduction.Using a variant of Moser's twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.展开更多
文摘In this paper,the existence of nonconstant oscillating periodic solution of differential difference e-quation with n time lags is stutied:x′(t)=-g(x(t))[f(x(t-τ1))+f(x(t-τ2))+…+f(x(t-τn))] the results of Paper[1-6] are extended and improved.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10825207, 11032009)by Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0968)
文摘Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if the rightmost characteristic root has negative real part. Based on the Lambert W function, this paper presents a simple algorithm for locating the rightmost characteristic root of periodic solutions of some nonlinear oscillators with large time delay. As application, the proposed algorithm is used to study the primary resonance and 1/3 subharmonic resonance of the Duffing oscillator under harmonic excitation and delayed feedback, as well as the control problem of the van der Pol oscillator under harmonic excitation by using delayed feedback, with a number of case studies. The main advantage of this algorithm is that though very simple in implementation, it works effectively with high accuracy even if the delay is large.
基金supported by the National Natural Science Foundation of China(Grant Nos.41174134 and 41274156)the National Basic Research Program of China("973"Project)(Grant No.2011CB811405)
文摘In this work,the ionospheric variability is analyzed by applying the wavelet decomposition technique to the noontime fo F2,F10.7,interplanetary magnetic field(IMF)Bz,Ap,and lower thermospheric temperature at pressure of 10?4 h Pa in 2002.Results show that the variance of periodic oscillations in the ionosphere is largest in the 2–4-day period and declines with the increase of the period.The maximum variance of the periodic oscillations in solar irradiation is in the 16–32-day period.For geomagnetic activities,most of the variance is about equally distributed on intervals of periods shorter than 32 days.Variance distributions of IMF Bz and lower thermospheric temperature are similar to those of the ionosphere.They show the maximum in the 2–4-day period and decline with the increase of the period.By analyzing the distributions of the variances,the potential connections between the ionosphere and the external sources are discussed.
文摘By using some analytical techniques, modified inequalities and Mawhin＇s continuous theorem of coincidence degree theory, some simple sufficient conditions for the existence of at least one positive almost periodic solution of a generalized Mackey-Glass model of respiratory dynamics are obtained. Further, the globM attractivity of positive almost periodic solution of the above model is also studied. To the best of the author＇s knowl- edge, so far, the result of this paper is completely new. Finally, three examples are given to illustrate the main results in this paper.
基金supported by the National Natural Science Foundation of China(No.10325103)the Chinese Scholarship Council(No.201206010092)
文摘In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g and e are regular, described precisely in the introduction.Using a variant of Moser's twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.
