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安徽师大学报:自然科学版宝鸡文理学院学报:自然科学版北京大学学报:自然科学版北京理工大学学报北京理工大学学报:英文版北京师范大学学报:自然科学版逼近论及其应用:新辑,英文版长沙电力学院学报:自然科学版长沙交通学院学报重庆师范学院学报:自然科学版纳粹教学与应用数学(西北大学)大连理工大学学报代数集刊:英文版(北京)电子科技大学学报东北大学学报:自然科学版乐北师大学报:自然科学版东北数学:英文版(吉林大学)东南大学学报东南大学学报:英文版非线性科学与数值模拟通讯:英文版福建师范大学学报:自然科学版福… 相似文献
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This paper is a continuation of "Complex Dynamics in Physical Pendulum Equation with Suspension Axis Vibrations"[1].In this paper,we investigate the existence and the bifurcations of resonant solution for ω0:ω:Ω ≈ 1:1:n,1:2:n,1:3:n,2:1:n and 3:1:n by using second-order averaging method,give a criterion for the existence of resonant solution for ω0:ω:Ω ≈ 1:m:n by using Melnikov's method and verify the theoretical analysis by numerical simulations.By numerical simulation,we expose some other interesting dynamical behaviors including the entire invariant torus region,the cascade of invariant torus behaviors,the entire chaos region without periodic windows,chaotic region with complex periodic windows,the entire period-one orbits region;the jumping behaviors including invariant torus behaviors converting to period-one orbits,from chaos to invariant torus behaviors or from invariant torus behaviors to chaos,from period-one to chaos,from invariant torus behaviors to another invariant torus behaviors;the interior crisis;and the different nice invariant torus attractors and chaotic attractors.The numerical results show the difference of dynamical behaviors for the physical pendulum equation with suspension axis vibrations between the cases under the three frequencies resonant condition and under the periodic/quasi-periodic perturbations.It exhibits many invariant torus behaviors under the resonant conditions.We find a lot of chaotic behaviors which are different from those under the periodic/quasi-periodic perturbations.However,we did not find the cascades of period-doubling bifurcation. 相似文献
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柯西不等式的推广及其应用 总被引:5,自引:0,他引:5
柯西不等式的推广及其应用徐幼明(湖北省浠水师范436200)柯西不等式是人们熟知的重要不等式.柯西不等式有如下的推广:当且仅当a11:a12:…:a1m=a21:a22:…:a2n=…=am1:am2:…:amn时等号成立.笔者认为,若将此定理作进一... 相似文献
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