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函数f(x)=|a-2x|的动力系统及其在二位黑洞数问题中的应用
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作者 周持中 《岳阳大学学报》 CAS 1991年第1期3-10,共8页
本文主要研究动力系统f:[o、a]→[o、a](a>o),x|→|a-2x|到的周期轨数,并对确定的奇数n研究了A_n={x|x/a=m/n,m<n,m∈z^+}中所含的周期轨数,利用所得结果彻底解决了r进制二位数中黑洞的个数与周长问题。
关键词 动力系统 黑洞 周期轨数
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Analytical Hopf Bifurcation and Stability Analysis of T System 被引量:2
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作者 Robert A.VanGorder S.Roy Choudhury 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第4期609-616,共8页
Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following th... Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes. 展开更多
关键词 extended Hopf bifurcation analysis method of multiple scales T system stability analysis
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CODIMENSION 3 BIFURCATIONS OFHOMOCLINIC ORBITS WITH ORBITFLIPS AND INCLINATION FLIPS 被引量:4
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作者 SHUISHULIANG ZHUDEMING 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2004年第4期555-566,共12页
The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is nonprincipal in the meanings that its positive semi-... The homoclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near the homoclinic orbit. This homoclinic orbit is nonprincipal in the meanings that its positive semi-orbit takes orbit flip and its unstable foliation takes inclination flip. The existence, nonexistence, uniqueness and coexistence of the 1-homoclinic orbit and the 1-periodic orbit are studied. The existence of the twofold periodic orbit and three-fold periodic orbit are also obtained. 展开更多
关键词 BIFURCATION Homoclinic orbit Orbit flip Inclination flip Periodic orbit
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Dynamics of surface motion on a rotating massive homogeneous body 被引量:6
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作者 LIU XiaoDong BAOYIN HeXi MA XingRui 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2013年第4期818-829,共12页
It is of great interest to study the dynamical environment on the surface of non-spherical small bodies, especially for asteroids. This paper takes a simple case of a cube for instance, investigates the dynamics of a ... It is of great interest to study the dynamical environment on the surface of non-spherical small bodies, especially for asteroids. This paper takes a simple case of a cube for instance, investigates the dynamics of a particle on the surface of a rotating homogeneous cube, and derives fruitful results. Due to the symmetrical characteristic of the cube, the analysis includes motions on two different types of surfaces. For each surface, both the frictionless and friction cases are considered. (i) Without consideration of friction, the surface equilibria in both of the different surfaces are examined and periodic orbits are derived. The analysis of equilibria and periodic orbits could assist understanding the skeleton of motions on the surface of asteroids. (ii) For the friction cases, the conditions that the particle does not escape from the surface are examined. Due to the effect of the friction, there exist the equilibrium regions on the surface where the particle stays at rest, and the locations of them are found. Finally, the dust collection regions are predicted. Future work will extend to real asteroid shapes. 展开更多
关键词 surface motion CUBE ASTEROIDS EQUILIBRIA periodic orbits equilibrium regions non-spherical bodies stability gravity
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