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1.
In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution (xs(t), 0, zs(t)) is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period τ, the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex. 相似文献
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In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model. 相似文献
4.
在金属层表面引入微结构以实现对Z箍缩等离子体形成和发展过程中不稳定性的调控具有重要研究价值.在“强光一号”装置上(峰值电流~1.4 MA,上升时间~100 ns),开展了针对具有一维周期性凹槽调制结构的金属薄膜的电爆炸实验研究.实验负载采用外推型平面结构,基底为30μm厚铝膜,刻蚀周期为2 mm,刻蚀深度约为10μm.通过激光阴影成像、激光干涉成像和可见光自辐射成像等系统进行联合诊断.实验结果表明刻蚀结构对等离子体发展过程的不稳定性特征产生了明显调制作用,原本征波长也受到抑制,微结构周期对不稳定结构波长产生趋同效应;未刻蚀一侧边界层同样受刻蚀层结构的影响,在不稳定结构上表现出相似形貌,且内外侧不稳定性特征的耦合关联性增强;刻蚀凹槽处在爆炸过程中膨胀更为迅速,形成的表面等离子体结构与初始结构反相;在刻蚀结构的几何突变处会形成细长的等离子体喷流,在二分之一刻蚀波长处出现波谱特征峰.理论分析表明电流密度调制造成电热不稳定性分布改变是调控作用产生的重要原因. 相似文献
5.
以经典BZ化学反应体系的三变量Oregonator模型及电极过程动力学为基础,提出了外控弱周期电极电流约束下电极BZ反应体系与体相BZ反应体系相互耦合的动力学模型.在体相处于稳定定态参数条件下,系统地研究了外控弱周期电流约束下电极BZ反应体系中的动力学行为,定量分析了电流慢变流型上的准定态稳定性及有利于出现极限环振荡区域.研究表明,与以前所报道的外控弱周期电位约束情况类似,在外控弱周期电流约束下电极BZ反应体系中的极限环振荡区域亦发生了蜕变,但体系对外控电流约束中的这种持续性之周期扰动的响应表现在两个方面:有利于出现极限环振荡区域的缩变及原非振荡区胁迫振荡的出现. 相似文献
6.
小孔周期性泄流的实验与分析 总被引:8,自引:2,他引:6
通过对小孔泄流的周期性研究.发现泄流周期随着时间进程变化趋于增大,小孔的直径越大泄流周期越小,不相容的液体间不能形成小孔周期性泄流,并分析了有关现象. 相似文献
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9.
SAXS and WAXD study of periodical structure for polyacrylonitrile fiber during coagulation 下载免费PDF全文
Small angle X‐ray scattering (SAXS) and wide angle X‐ray diffraction (WAXD) were adopted to investigate the formation and development of high order structure within polyacrylonitrile (PAN) precursor during coagulation. The scattering signal came from the microvoids and long period structure was separated reasonably by the analog computation method of decomposition of the one‐dimensional profile. Based on the established methodology, the statistic parameters of long period structure, such as length of the long period structure, crystalline region and amorphous region, were obtained by the analysis of correlation function. The results indicated that during the coagulation, the length of long period of the nascent coagulated fiber was 56.1 nm (meridional direction) and 35.6 nm (equatorial direction), respectively. The evolution of the long period during the coagulation was also discussed by combining WAXD data. With the processing of coagulation, the long period was decreased since the crystallinity increased. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
10.
提出了以圆筒扭转力学模型为基础, 预测周期性多孔材料等效剪切模量及其研究尺寸效
应的一种简单有效计算方法. 以方形孔和圆形孔两种典型多孔材料为例进行了数值计算求解;
同时, 建立了几何参数随体胞尺寸缩放因子$n$的解析关系, 证明了两种构型的周期性多孔材
料的等效剪切模量均随尺寸缩放因子$n$的增大而减小. 当$n \to \infty
$时, 即体胞尺寸相对整体结构无限小时, 多孔材料的等效剪切模量趋近收敛于一个恒定值;
当体胞的材料体分比增大时, 多孔材料等效剪切模量也随之增大. 此外, 依据周
期性多孔材料的结构对称特性, 使用体胞子结构有限元计算模型进行等效剪切模量及其尺寸
效应的预测, 极大地提高了计算效率. 相似文献