Nonlinear Dynamics and Bifurcations of a Supercavitating Vehicle

In this effort, a numerical study of the bifurcation behavior of a supercavitating vehicle is conducted. The vehicle model is nonsmooth; this is a result of the planing force acting on the vehicle. With a focus on dive-plane dynamics, bifurcations with respect to a quasi-static variation of the cavitation number are studied. The system is found to exhibit rich and complex nonlinear dynamics including nonsmooth bifurcations such as the grazing bifurcation; smooth bifurcations such as Hopf bifurcations, cyclic fold bifurcations, and period-doubling bifurcations; and aperiodic behaviors such as transient chaotic motions and chaotic crises. The tailslap phenomenon of the supercavitating vehicle is identified as the consequence of a Hopf bifurcation followed by a grazing event. It is shown that the occurrences of these bifurcations can be delayed or triggered earlier by using dynamic linear feedback control laws employing washout filters.     

Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation

This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincaré map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using non-feedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to period-motions by adding an excitation term.     

渤海赤潮藻类生态动力学模型的非线性动力学研究

基于渤海典型赤潮藻类——中肋骨条藻 ,考虑浮游动物的捕食、光照及营养物质的作用 ,建立了渤海湾的浮游动物—藻类—营养物质三者的动力学模型。运用现代非线性动力学理论着重分析了模型的稳定性及分岔行为。研究了多个参数对藻类生长的影响 ,发现某些参数对藻类的生长影响不大 ,而某些参数则会致使藻类模型出现分岔乃至混沌行为 ,并给出了这些参数的阀值 ,这与赤潮的形成 (爆发性增殖 )密切相关 ;并根据渤海湾的赤潮数据进行了有效的数值模拟 ,所得结果对于研究赤潮的形成机理有一定的参考价值     

海洋生态系统动力学模型的稳定性和Hopf分岔研究

海洋生态系统动力学模型的可预测性是模型应用的重要限制因子之一,而模型稳定性则是模型可预测性的前提。本文提出了一个基于降维理论的方法,用于研究质量守恒的营养盐-浮游植物-浮游动物-碎屑(NPZD)这类海洋生态系统动力学模型的稳定性和Hopf分岔。研究结果显示,NPZD模型的非奇异平衡点是稳定的,而当模型参数在临界值附近变动时可能会发生Hopf分岔。同时,本文采用数值模拟的方法对该理论分析结果进行了实例验证。本文提出的基于降维理论的方法能够从理论上有效分析质量守恒系统的稳定性问题和Hopf分岔。     

分数阶混沌系统与整数阶混沌系统之间的同步

基于追踪控制的思想,利用分数阶系统稳定性理论,实现了分数阶混沌系统与整数阶混沌系统之间的混沌同步,给出了补偿器和反馈控制器的选择方法. 以三维分数阶Chen系统和三维整数阶Lorenz混沌系统之间的混沌同步为例进行了数值仿真和电路仿真. 研究表明了该同步方法的有效性.     

Surface manifestations of internal waves investigated by a subsurface buoyant Jet: 1. The mechanism of internal-wave generation

In a large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences, we have performed a major laboratory simulation of the nonstationary dynamics of buoyant turbulent jets generated by wastewater flows from underwater collector diffusers. The interaction of buoyant jets with the pycnocline leads to an active generation of internal waves. An analysis of the dependence of wave amplitude on the control parameter proportional to the rate of liquid flow from the collector diffuser has indicated that this dependence is adequately described by a function that is characteristic for the presence in the Hopf bifurcation system, which occurs for a soft actuation mode of self-oscillations of the globally instable mode. To check the conditions for the actuation of the globally instable mode, we have performed an auxiliary experiment in a small reservoir with a salt stratification formulated similar to the experiment in the big reservoir. Using the particle image velocimetry (PIV) method, we have measured the velocity field in the buoyant jet and constructed the profiles of transverse velocity in several sections. When the jet approaches the pycnocline, a counterflow is generated at the edges. A stability analysis for the resulting profiles of flow velocities performed by the method of normal modes has revealed that, for the jet portions with counterflow, the condition of absolute instability by the Briggs criterion for axisymmetric jet oscillations is satisfied, which testifies to the fact that the globally instable mode is actuated. The estimates for oscillation frequencies of the globally instable mode are well consistent quantitatively with the measured spectrum of jet oscillations.     

一类相对转动时滞非线性动力系统的稳定性分析

建立了具有时变刚度、非线性阻尼和谐波激励的一类相对转动时滞非线性动力系统的动力学方程.采用多尺度法推导出时滞动力系统的分岔响应方程,运用奇异性理论研究系统结构稳定性,得到主共振稳态响应方程的转迁集以及不同参数下分岔曲线的拓扑结构.应用Hopf分岔理论讨论了时滞动力系统动态稳定性,给出了系统产生极限环的条件,最后用数值模拟的方法研究了时滞参数对系统极限环幅值的影响.     

油轮“鱼尾”运动及Hopf分叉算法

本文使用一个六阶三自由度的非线性数学模型，研究单点系泊（ＳＰＭ）系统“鱼尾”运动，对系统的平衡状态，及其在风向角、风速、流速、缆绳长度等参数变化时规律，进行了一系列的分析，同时，指出了静平衡系泊力的变化规律。为了研究系统平衡态的稳定性，文中选择缆绳长度ｌ为分叉参数，分析了在不同参数值下，系统Ｊａｃｏｂｉａｎ矩阵的各组特征值的变化情况，并求出了系统的Ｈｏｐｆ分叉点。最后，本文利用Ｈｏｐｆ分叉理论，求出了系统的Ｈｏｐｆ分叉周期解。     

随机波浪荷载作用下海洋平台的前馈-反馈振动控制研究

该文研究线性前馈 -反馈控制策略对海洋平台振动控制的有效性。线性前馈 -反馈控制只有当输入荷载为白噪声过程时 ,所实施的控制才是最优的 ,因此该文采用一白噪声过程通过滤波器来近似随机波浪力谱 ,并将海洋平台 -主动控制系统的动力学方程转化为符合随机最优控制要求的增广状态空间表达形式。依据设计目标中对安全性以及经济性的权衡 ,通过使二次型控制目标函数最小化 ,推导出了随机最优控制力的计算方法 ,从而实现了最优控制的目的。在频率域上分析了海洋平台受控后的振动响应 ,结合典型的海洋天然气生产平台算例 ,将前馈 -反馈控制与反馈控制、TMD控制加以比较 ,总结了前馈 -反馈控制的特点及其优越性     

On freshwater-dependent bifurcations in box models of the interhemispheric thermohaline circulation

Conceptual box models of the interhemispheric thermohaline circulation are studied with respect to bifurcations. Freshwater fluxes are the main control parameters of the system: they determine the stable states and transitions between stable states of the large-scale thermohaline circulation. In this study of interhemispheric box models both numerical and analytical methods are used to investigate transition mechanisms of the thermohaline circulation. The box model examined first is an interhemispheric four-box model. It is shown that the two bifurcations where the present THC can become unstable, the saddle-node and the Hopf bifurcation, depend in a different way on hemispheric freshwater fluxes. A reduction of the model variables leads to the conclusion that two fixed freshwater fluxes between three surface boxes are the model feature responsible for the bifurcation behaviour found. The significance of the Hopf bifurcation for the stability of the thermohaline circulation is discussed.     

海洋浮游生态系统模型的稳态非线性动力学研究

以Logistic模型为基础,考虑捕捞行为及其所造成的污染对浮游生物的削弱作用,并考虑浮游生态系统具有一定的自净能力,建立了一个新的海洋浮游生态系统非线性动力学模型。分析了模型的非线性动力学特性,并得出了模型的稳定性条件和发生Hopf分岔条件,在此基础上,深入分析了捕捞强度参数的变化对系统稳态的影响,并且用数值模拟验证了理论分析结果的正确性。     

Inelastic buckling of thick-walled circular conical shells under external hydrostatic pressure

The paper reports on a theoretical and an experimental study into the collapse of three thick-walled circular conical shells, which were tested to failure under external hydrostatic pressure. All three vessels failed by plastic non-symmetric bifurcation buckling. Two theoretical analyses were carried out, both based on the finite element method. One of the theoretical analyses was based on inelastic non-symmetric bifurcation buckling and the other analysis was based on plastic axisymmetric buckling. Both of these theoretical analysis and the experimental observations appeared to indicate that there is a link between plastic non-symmetric bifurcation buckling and plastic axisymmetric buckling.     

多频参激—涡激联合作用下顶张力立管分岔分析

复杂海洋环境中,顶张力立管顶部平台受到不同分量叠加的波浪作用,导致其轴向张力与多个频率相关,系统产生多频参激与涡激的联合振动,其动力学行为变得更为复杂,尤其是分岔和混沌等非线性振动特性有待进一步分析。首先,基于欧拉—伯努利梁理论,引入范德波尔尾流振子,建立和推导受多频参激—涡激联合作用下立管的动力学模型及其运动微分方程;接着,利用伽辽金法得到离散后的常微分方程组,采用多尺度法得到系统共振响应的调谐方程;最后,通过数值算例探究系统在多源和多频载荷联合作用下的共振响应。结果表明：对于多频参数激励,其中一个参数激励幅值在立管振动中起主导作用,而另一个会引起分岔的位置、数量和性质发生改变;随质量—阻尼参数增大,系统共振响应幅值整体先增大后减小,各分岔点出现的位置整体先向泄涡频率较大处移动,随后向泄涡频率较小处移动;质量—阻尼参数的变化还可能诱使系统发生倍周期分岔和混沌现象,危害结构安全。此外,采用直接数值积分求解微分方程组,验证近似分析结果,两者吻合较好。     

The maximum likelihood ensemble filter performances in chaotic systems

The performance of the maximum likelihood ensemble filter (MLEF), is investigated in the context of generic systems featuring the essential ingredients of unstable dynamics and on a spatially extended system displaying chaos. The main objective is to clarify the response of the filter to different regimes of motion and highlighting features which may help its optimization in more realistic applications. It is found that, in view of the minimization procedure involved in the filter analysis update, the algorithm provides accurate estimates even in the presence of prominent non-linearities. Most importantly, the filter ensemble size can be designed in connection to the properties of the system attractor (Kaplan–Yorke dimension), thus facilitating the filter setup and limiting the computational cost by using an optimal ensemble. As a corollary, this latter finding indicates that the ensemble perturbations in the MLEF reflect the intrinsic system error dynamics rather than a sampling of realizations of an unknown error covariance.     

集合资料同化方法的理论框架及其在海洋资料同化的研究展望

在海洋动力系统的数值模拟中,海洋资料同化是一种能够有效融合多源海洋观测资料和数值模式的方法。它不仅可以显著地提高数值模拟的效果,构造海洋再分析资料场,还能有效减少海洋和气候预报时模式初始条件的不确定性。因此,海洋资料同化对于海洋研究和业务化应用具有非常重要的意义。资料同化方法的研究一直是大气、海洋科学的热门课题之一。其中,集合卡尔曼滤波器(EnKF)是一种有效的资料同化方法,自提出以来经过了20多年的发展和改进,已经在海洋资料同化中得到了广泛的研究和应用。近年来,随着动力模式的不断发展和计算能力的提高,粒子滤波器由于不受模型线性和误差高斯分布假设的约束,也逐渐成为了当前资料同化方法研究的热点。本文分析和总结了目前关于集合卡尔曼滤波器和粒子滤波器的一些最新理论研究结果,在贝叶斯滤波理论的框架下讨论了这两类算法的关联和区别,以及各自在资料同化实践中的优势和不足。在此基础上,我们探讨了粒子滤波器应用于海洋模式资料同化的主要困难和目前可行的一些解决方法,展望了集合资料同化方法研究的新趋势,为集合资料同化方法的进一步发展和应用提供理论基础。     

随机波浪作用下海洋平台主动控制的时滞补偿研究

基于预测控制理论，研究了适用于海洋平台的时滞补偿控制算法。该方法借助于随机波浪力的近似公式和卡尔曼滤波原理，推导出了随机波浪力向前一步预测公式，同时采用卡尔曼滤波方程，实现了对状态向量向前一步预测。利用随机波浪力及状态向量的实时在线预测公式，推导出最优控制力向前一步预测的表达式。在此基础上，发展了不仅适用于反馈控制系统而且适用于前馈-反馈控制系统的时滞补偿算法。采用一典型海洋平台为数值算例，计算结果表明，该方法在一定时滞范围内对海洋平台主动控制中时滞的补偿效果是显著的。     

混沌系统的变结构同步控制

研究Lorenz混沌系统的同步控制问题,提出1种在多输入的情况下实现混沌同步的变结构控制算法.利用该算法设计的变结构同步控制律使得同步误差系统的运动在切换面上成为渐近稳定的滑动模态,从而较快的实现了混沌同步.通过对 Lorenz 混沌系统的理论分析和数值仿真,说明了该变结构同步控制策略的实用性和有效性.     

基于记忆电阻的Chua混沌电路的实现及动态性能分析

提出利用磁通量控制的记忆电阻和1个负电导来替代典型蔡氏混沌电路的非线性电阻,并对改进后电路的理论推导、数值仿真、分岔图l、yapunov指数谱等系统的基本动力学特性进行分析,结果显示,该系统可由马蹄混沌吸引子过渡为双涡卷混沌吸引子,混沌行为更为复杂。最后,利用FPGA技术实现了该电路,实验结果表明,该系统能够产生混沌吸引子。     

受扰线性系统的前馈-反馈最优控制

针对具有外部持续扰动的线性系统，研究前馈-反馈最优控制律的设计问题。给出了最优控制律的存在唯一性条件。并提出了最优控制律的设计算法。利用滤波器解决了前馈控制的物理不可实现问题。仿真结果表明，此算法易于实现，与传统的反馈最优控制相比对抑制外部扰动具有较强的鲁棒性。     

具有变时滞的非线性系统的时滞相关非脆弱保成本控制

对于一类具有变时滞和控制器增益摄动的非线性系统,研究非脆弱保成本控制问题。在控制器参数存在加法摄动和乘法摄动2种情况下,设计1个无记忆状态反馈非脆弱保成本控制律,使闭环系统渐近稳定,并且闭环性能指标不超过某个确定的上界。利用线性矩阵不等式方法,给出时滞相关的非脆弱保成本控制律存在的条件和控制器的设计方法。