J.Kaplan and J.Yorke's method is extended to establish the exis- tence of many and infinitely many periodic solutions for the DDEs (t) =±f(x(t-1))±f(x(t-2))and (t)=±f(x(t-1).
By introducing the periodic parameter-switching signal to the Lorenz oscillator, a switched dynamic model is established. In order to investigate the mechanism of the behaviors of the whole system, bifurcation sets of...By introducing the periodic parameter-switching signal to the Lorenz oscillator, a switched dynamic model is established. In order to investigate the mechanism of the behaviors of the whole system, bifurcation sets of the subsystems are derived and the Poincar6 map of the switched system is defined by suitable local sections and local maps. Under certain parameter conditions, symmetric periodic oscillations may be observed. With the variation of parameter, the symmetry-breaking bifurcation mecha- nisms of the symmetric periodic oscillations can be understood by calculating the associated maximal Lyapunov exponent and Floquet multiplies. Meanwhile, the parameter values of the related local bifurcations, such as saddle-node, pitchfork and peri- od-doubling bifurcations are calculated based on the Floquet multiplies.展开更多
Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all perio...Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all periodical maps on Σ2. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair(S3, Σg). To do this the authors first list all periodic maps on Σ2, and indeed the authors exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself should be interesting. A by-product is that for each even g,the maximum order periodic map on Σg is extendable, which contrasts sharply with the situation in the orientation preserving category.展开更多
This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the differenc...This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the difference of the evolution with the linear evolution is in Hs1 （T） for all times, with at most polynomial growing HS1 norm. Unlike Korteweg-de Vries （KdV） equation, there are less symmetries of the Benjamin system, especially for the resonant function. The new ingredient is that we need to deal with some new difficulties that are caused by the lack of symmetries.展开更多
The present paper investigates the asymmetrical variability of the location of the north and the south equatorial ionization anomaly(EIA) crests in the East-Asian sector,along with their association with simultaneous ...The present paper investigates the asymmetrical variability of the location of the north and the south equatorial ionization anomaly(EIA) crests in the East-Asian sector,along with their association with simultaneous observations of equatorial electrojet(EEJ) strength,geomagnetic activity index,and solar flux index during the 2002-2003 sudden stratospheric wanning(SSW) event.Analysis of these observations indicates the existence of a large-scale quasi 16-day periodic meridional movement in both EIA crests,and also reveals a strong correlation between the quasi 16-day oscillation in geomagnetic latitudes of the EIA crest and EEJ strength.The latitude of the northern/southern EIA crest and the EEJ strength indicate that obvious synchronous periodic oscillations were in-phase in the northern and southern hemisphere when the SSW occurred.In addition,it is also found that both the EIA crest location and amplitude of the periodic movement of the EIA locations exhibit hemispheric asymmetry.The amplitude of the periodic movement of the EIA location in the southern hemisphere is larger than that of the northern hemisphere,and the southern EIA crest is further off from the equator than the north one.Understanding these asymmetries requires a combination of mechanisms that involve at least trans-equator meridional winds and the position of a sub-solar point;however,potential disturbances in neutral winds associated with the SSW may additionally complicate the equatorial ionospheric dynamics.展开更多
A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the ra...A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained.The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed,that is to say,a circular cavity will form if the suddenly applied radial tensile load exceeds a certain critical value;dynamically,it is proved that the formed cavity will present a nonlinearly periodic oscillation,which is essentially different from the singular periodic oscillation of the formed cavity in an incompressible hyperelastic solid sphere.Numerical simulations show the effects of prescribed radial tension,material parameter and tensile load on critical ten-sile load describing cavity formation and periodic oscillation of the pre-strained circular sheet.展开更多
We construct exact stationaxy solutions to the one-dimensional coupled Gross-Pitaevskii equations for the two-species Bose-Einstein condensates with equal intraspecies and interspecies interaction constants. Three typ...We construct exact stationaxy solutions to the one-dimensional coupled Gross-Pitaevskii equations for the two-species Bose-Einstein condensates with equal intraspecies and interspecies interaction constants. Three types of complex solutions as well as their soliton limits axe derived. By making use of the SU（2） unitary symmetry, we further obtain analytical time-evolving solutions. These solutions exhibit spatiotemporal periodicity.展开更多
文摘J.Kaplan and J.Yorke's method is extended to establish the exis- tence of many and infinitely many periodic solutions for the DDEs (t) =±f(x(t-1))±f(x(t-2))and (t)=±f(x(t-1).
基金supported by the National Natural Science Foundation of China (Grant Nos. 21276115, 11272135, 11202085)the Scientific Research Innovation Foundation of Jiangsu Province (Grant No. CXZZ13-0653)the Natural Science Foundation for Colleges and Universities of Jiangsu Province (Grant No. 11KJB130001)
文摘By introducing the periodic parameter-switching signal to the Lorenz oscillator, a switched dynamic model is established. In order to investigate the mechanism of the behaviors of the whole system, bifurcation sets of the subsystems are derived and the Poincar6 map of the switched system is defined by suitable local sections and local maps. Under certain parameter conditions, symmetric periodic oscillations may be observed. With the variation of parameter, the symmetry-breaking bifurcation mecha- nisms of the symmetric periodic oscillations can be understood by calculating the associated maximal Lyapunov exponent and Floquet multiplies. Meanwhile, the parameter values of the related local bifurcations, such as saddle-node, pitchfork and peri- od-doubling bifurcations are calculated based on the Floquet multiplies.
基金supported by the National Natural Science Foundation of China(No.10631060)
文摘Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all periodical maps on Σ2. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair(S3, Σg). To do this the authors first list all periodic maps on Σ2, and indeed the authors exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself should be interesting. A by-product is that for each even g,the maximum order periodic map on Σg is extendable, which contrasts sharply with the situation in the orientation preserving category.
基金supported by National Natural Science Foundation of China(Grant Nos.11171026 and 11271175)National Natural Science Foundation of Shandong Province(Grant No.ZR2012AQ026)
文摘This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs（T） initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s ＋ 1,3s ＋ 1}, the difference of the evolution with the linear evolution is in Hs1 （T） for all times, with at most polynomial growing HS1 norm. Unlike Korteweg-de Vries （KdV） equation, there are less symmetries of the Benjamin system, especially for the resonant function. The new ingredient is that we need to deal with some new difficulties that are caused by the lack of symmetries.
基金supported by the National Natural Science Foundation of China(Grant Nos.41274156, 41464006 & 41674157)Guangxi Natural Science Foundation(Grant No.2014GXNSFAA118282)+1 种基金L.Goncharenko and S R.Zhang have been supported through US National Science Foundation(Grant No. AGS-1132267)the Haystack Observatory was also supported through a cooperative agreement(Grant No.AGS-1242204) between the US National Science Foundation and MIT
文摘The present paper investigates the asymmetrical variability of the location of the north and the south equatorial ionization anomaly(EIA) crests in the East-Asian sector,along with their association with simultaneous observations of equatorial electrojet(EEJ) strength,geomagnetic activity index,and solar flux index during the 2002-2003 sudden stratospheric wanning(SSW) event.Analysis of these observations indicates the existence of a large-scale quasi 16-day periodic meridional movement in both EIA crests,and also reveals a strong correlation between the quasi 16-day oscillation in geomagnetic latitudes of the EIA crest and EEJ strength.The latitude of the northern/southern EIA crest and the EEJ strength indicate that obvious synchronous periodic oscillations were in-phase in the northern and southern hemisphere when the SSW occurred.In addition,it is also found that both the EIA crest location and amplitude of the periodic movement of the EIA locations exhibit hemispheric asymmetry.The amplitude of the periodic movement of the EIA location in the southern hemisphere is larger than that of the northern hemisphere,and the southern EIA crest is further off from the equator than the north one.Understanding these asymmetries requires a combination of mechanisms that involve at least trans-equator meridional winds and the position of a sub-solar point;however,potential disturbances in neutral winds associated with the SSW may additionally complicate the equatorial ionospheric dynamics.
基金supported by the National Natural Science Foundation of China (Grant Nos.10872045, 10721062)the Program for New Century Excellent Talents in University (Grant No.NCET-09-0096)the Fundamental Research Funds for Central Universities (Grant No.DC10030104)
文摘A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained.The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed,that is to say,a circular cavity will form if the suddenly applied radial tensile load exceeds a certain critical value;dynamically,it is proved that the formed cavity will present a nonlinearly periodic oscillation,which is essentially different from the singular periodic oscillation of the formed cavity in an incompressible hyperelastic solid sphere.Numerical simulations show the effects of prescribed radial tension,material parameter and tensile load on critical ten-sile load describing cavity formation and periodic oscillation of the pre-strained circular sheet.
基金Supported by funds from the Ministry of Science and Technology of China under Grant No.2012CB821403by National Natural Science Foundation of China under Grant No.11374036
文摘We construct exact stationaxy solutions to the one-dimensional coupled Gross-Pitaevskii equations for the two-species Bose-Einstein condensates with equal intraspecies and interspecies interaction constants. Three types of complex solutions as well as their soliton limits axe derived. By making use of the SU（2） unitary symmetry, we further obtain analytical time-evolving solutions. These solutions exhibit spatiotemporal periodicity.
