周期外力对频率涨落的过阻尼谐振子所作的功和能量随机共振

研究了周期外力对频率涨落的过阻尼谐振子系统作功的特点. 结果揭示了瞬时功率随时间的周期变化出现不对称性. 研究结果还揭示周期外力一个周期对系统所做的功随乘法噪声强度的变化出现非单调行为, 系统是否出现能量随机共振与抑制并存, 由乘法噪声与加法噪声之间互关联的符号决定. 关键词： 过阻尼谐振子 频率涨落 周期外力作功 能量随机共振与抑制     

非均匀圆柱壳中非线性波传播模型的同伦分析解法

圆柱形壳中非线性波传播问题的研究具有重要的理论和现实意义.本文用同伦分析方法,研究了描述非均匀圆柱壳中非线性波传播的一种新模型,得到了该模型的高精度近似孤波解和周期波解.这表明同伦分析方法是研究非线性波传播问题的一种十分有效的方法.     

用周期铁磁结构环作磁累积发生器的初始能源

 首先推导了描述铁磁体的磁场方程，并分析计算了圆筒型周期性永磁结构环内部所携带的磁能，研究了磁能与永磁体质量的关系。分析表明，采用内外径分别为60和90mm、长为60mm、质量约为30kg的四级周期永磁结构能够提供1kJ左右的磁能。这种结构有可能成为间接馈电磁累积发生器的初始能源。     

一类具时滞的厄尔尼诺-南方涛动充电-放电振子模型的Hopf分岔与周期解问题

研究了一类具时滞的厄尔尼诺-南方涛动充电-放电振子模型. 给出了产生Hopf分岔的临界时滞条件, 利用Mawhin重合度理论,探讨了该模型的周期解问题. 关键词： 时滞 厄尔尼诺-南方涛动模型 Hopf分岔 周期解     

竖直振动颗粒床中的倍周期运动

实验研究了竖直振动颗粒床中颗粒对容器底部的压力随振动强度的变化情况.发现压力随振动加速度的增加经历倍周期分岔，典型的分岔序列为：2P，4P，混沌，3P，6P，混沌，4P，8P，混沌.观察表明，伴随倍周期分岔现象，在颗粒床底部出现颗粒的聚集态.聚集态内颗粒密堆积在一起并作整体的上下运动.采用完全非弹性蹦球模型分析了颗粒对容器底的冲击力，并给出了倍周期分岔现象的一种解释. 关键词： 颗粒物质 混沌 倍周期分岔 非弹性碰撞     

外光注入半导体激光器实现重复速率可调全光时钟分频

采用Fabry-Perot半导体激光器作为全光时钟分频器件,利用光注入半导体激光器产生的非线性动力学特性,实现了光脉冲的重复速率在9.0 GHz到19.8 GHz范围内连续可调的全光时钟分频. 同时利用半导体激光器速率方程,对脉冲光注入半导体激光器产生时钟分频进行了数值模拟. 实验和模拟结果表明半导体激光器在光注入的驱动下处于一周期振荡状态,当一周期振荡的二次谐波频率接近脉冲光的重复速率时,其二次谐波和基频被脉冲光同时锁定,此时将输出频率为脉冲光重复速率一半的时钟信号. 同时研究了波长失谐量和注入光功率对 关键词： 周期振荡 时钟分频 光注入 非线性动力学     

周期信号傅里叶分析一种实验观测方法

介绍了用两只动圈扬声器组成谐波装置，用于对周期信号进行傅里叶分析。讨论了谐波共振时振幅的特性。     

捕食模型正周期解存在性的一个注记

利用重合度理论中的延拓定理讨论了多滞量捕食模型(dN_1(t))/dt=N_1(t)[r_1(t)-a_(11)(t)N_1(t-τ_1(t))-a_(12)(t)N_2(t-τ_2(t))] (dN_2(t))/dt=N_2(t)[-r_2(t)+a_(21)(t)N_1(t-τ_3(t))]的正周期解的存在性,得到了保证上述系统周期解存在的一组时滞依赖的充分条件,补充和完善了已有学者的工作.     

Complex dynamics in physical pendulum equation with suspension axis vibrations

The physical pendulum equation with suspension axis vibrations is investigated. By using Melnikov＇s method, we prove the conditions for the existence of chaos under periodic perturbations. By using second-order averaging method and Melinikov＇s method, we give the conditions for the existence of chaos in an averaged system under quasi-periodic perturbations for Ω = nω ＋ εv, n = 1 - 4, where ν is not rational to ω. We are not able to prove the existence of chaos for n = 5 - 15, but show the chaotic behavior for n = 5 by numerical simulation. By numerical simulation we check on our theoretical analysis and further exhibit the complex dynamical behavior, including the bifurcation and reverse bifurcation from period-one to period-two orbits; the onset of chaos, the entire chaotic region without periodic windows, chaotic regions with complex periodic windows or with complex quasi-periodic windows; chaotic behaviors suddenly disappearing, or converting to period-one orbit which means that the system can be stabilized to periodic motion by adjusting bifurcation parameters α, δ, f0 and Ω; and the onset of invariant torus or quasi-periodic behaviors, the entire invariant torus region or quasi-periodic region without periodic window, quasi-periodic behaviors or invariant torus behaviors suddenly disappearing or converting to periodic orbit; and the jumping behaviors which including from period- one orbit to anther period-one orbit, from quasi-periodic set to another quasi-periodic set; and the interleaving occurrence of chaotic behaviors and invariant torus behaviors or quasi-periodic behaviors; and the interior crisis; and the symmetry breaking of period-one orbit; and the different nice chaotic attractors. However, we haven＇t find the cascades of period-doubling bifurcations under the quasi-periodic perturbations and show the differences of dynamical behaviors and technics of research between the periodic perturbations and quasi-periodic perturbations.     

Banach 空间中一阶周期边值问题的广义解

In this paper, the authors study the periodic boundary value problems of a class of nonlinear integro-differential equations of mixed type in Banach space with Carath′eodory's conditions. We arrive at the conclusion of the existence of generalized solutions between general- ized upper and lower solutions, and develop the monotone iterative technique to find generalized extremal solutions as limits of monotone solution sequences in Banach space.