有障碍圆形浮力射流的绕流流态研究

针对静止环境中有障碍圆形浮力射流出现的正常绕流现象与非正常绕流现象（反射与分叉现象）,分析了其主要的3个影响因素:障碍盘直径D/d（D和d分别是障碍盘和射流出口的直径）,射流出口密度Froude数以及障碍盘离射流孔口的距离H/d与发生非正常绕流之间的相互关系．得到了H/d=2,4,6,8在不同D/d值时发生非正常绕流的临界密度Froude数．对直径为D/d的障碍盘,当其离射流孔口的距离H/d达到某一值时,流动仅为正常绕流流态．基于大量计算给出了不同障碍盘所要求的H/d值,综合以上因素得到了临界密度Froude数的拟合公式．对非正常绕流中射流出现反射与分叉的规律性进行了探讨．对D/d=1的有障碍浮力射流进行的数值计算表明,所有工况下的流态均为正常绕流,并得到了不同H/D条件下的轴线稀释度．     

液面的分叉与稳定性分析

本文讨论液体层在内聚力以及液体与外界相互作用下,其表面形状出现的一类分叉现象。利用分叉的基本理论,我们得到了这类现象产生的必要条件。接着,我们给出了在分叉点附近的奇异摄动解。最后,利用极小势能原理讨论了分叉解的稳定性。     

细长体截面绕流的稳定性及扰动的影响

应用拓扑结构的稳定性理论,分析了细长旋成体截面绕流的结构稳定性．在分析时取极限流线作为流场的内边界,并证明极限流线的鞍点-鞍点连接是拓扑结构稳定的A·D2通过分析发现,由于旋成体背涡的发展,导致截面流场拓扑结构变化,由稳定对称旋涡流态变成不稳定对称旋涡流态．此时流场中存在空间的鞍点-鞍点连接的不稳定拓扑结构,在小扰动下出现分叉,变成稳定非对称旋涡流态,形成非对称背涡．并应用开折理论分析了扰动对流场结构的影响．     

可瘪管定常流动的若干新现象

在较宽的参数范围内进行了可瘪管定常流动实验。当流速-波速比较高时,发现了若干新现象:(ⅰ)当管道开始被压瘪,或已压瘪的管道即将完全开启时,流态发生突变,从定常流变为脉动流(或相反);同时,流量、压力发生阶跃;(ⅱ)压差-流量曲线出现双峰;(ⅲ)在正阻尼区亦可能发生持续的振荡。讨论了实变发生的原因和激振机理。     

加权p-Laplace方程解的整体分叉问题

该文利用指标理论，谱理论以及标准分叉定理，研究了加权索伯列夫空间中的p Laplace方程初值问题的解的整体分叉现象。     

经过修正的层次流流动的流动稳定性问题(Ⅱ)——经过修正的平行剪切流的线性稳定性研究

本文根据文[1]给出的经过修正的层流流动的流动稳定性理论及平行剪切流中平均速度的一类修正剖面,研究了平行剪切流的线性稳定性性质,对于平面Couette流动和圆管Poiseuill流动,首次得到了二维扰动和轴对称扰动也能造成失稳的结果,并给出了这两种流动在某种定义下的中性曲线.     

细长体截面绕流中的一种临界状态

应用拓扑分析的方法研究了细长体截面绕流拓扑结构的演变过程．指出随着细长体背涡的发展,导致截面流场的拓扑结构发生变化,会出现一种临界流动状态．在这种临界流态下,流场中会出现一种高阶奇点．这种高阶奇点的指数为-3/2．这种高阶奇点是结构不稳定的,稍有扰动就会产生分叉,使流场的拓扑结构发生变化．     

三个自变量下强间断相互作用的精确计算

本文提出了能精确计算三个自变量下双曲型方程组强间断相互作用的比较完整的方法,给出了三维定常流中激波与激波的相互作用、激波与切向间断的相互作用的一些计算结果.另外还提出了一种基于特征理论的能自动精确确定嵌入激波的方法.给出了定常流中悬挂激波的计算结果.     

一类碰撞振动系统的余维二分叉和Hopf分叉*

本文研究弹簧质量系统对无穷大平面碰撞振动的分叉问题。证明了在接近完全弹性碰撞和在一些特殊的频率比附近,存在余维二分叉现象。利用映射的正则型理论,将Poincaré映射变换成含两个参数的正则型,通过分析该正则型,我们得到周期倍化分叉、周期1点、2点的Hopf分叉。并进行了数值验证。     

一个具有阶段结构的竞争系统中自食的周期性作用

利用重合度理论中的延拓定理，讨论了一个具有阶段结构的竞争系统，当发生自食现象时，给出了保证周期解存在的充分条件．     

具有饱和治疗的离散SEIS结核病模型的动力学性态

研究了一类具有饱和治疗的离散SEIS传染病模型的动力学性态.利用再生矩阵的方法定义了模型的基本再生数,直接计算得到了无病平衡点和地方病平衡点的存在性;利用线性化矩阵和Jury判据讨论了平衡点的稳定性;并讨论了模型可能发生的后向分支现象,也通过数值模拟展示了模型的动力学性态.     

Complex dynamics of a Holling type II prey–predator system with state feedback control

The complex dynamics of a Holling type II prey–predator system with impulsive state feedback control is studied in both theoretical and numerical ways. The sufficient conditions for the existence and stability of semi-trivial and positive periodic solutions are obtained by using the Poincaré map and the analogue of the Poincaré criterion. The qualitative analysis shows that the positive periodic solution bifurcates from the semi-trivial solution through a fold bifurcation. The bifurcation diagrams, Lyapunov exponents, and phase portraits are illustrated by an example, in which the chaotic solutions appear via a cascade of period-doubling bifurcations. The superiority of the state feedback control strategy is also discussed.     

Stability analysis of shear-thinning flow between rotating cylinders

Stability of the shear thinning Taylor–Couette flow is carried out and complete bifurcation diagram is drawn. The fluid is assumed to follow the Carreau–Bird model and mixed boundary conditions are imposed. The low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. It is observed, that the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the shear thinning effects increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, shear-thinning Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Complete flow field together with viscosity maps are given for different scenarios in the bifurcation diagram.     

Dynamics of a ratio‐dependent stage‐structured predator‐prey model with delay

In this paper, we investigate the dynamics of a time‐delay ratio‐dependent predator‐prey model with stage structure for the predator. This predator‐prey system conforms to the realistically biological environment. The existence and stability of the positive equilibrium are thoroughly analyzed, and the sufficient and necessary conditions for the stability and instability of the positive equilibrium are obtained for the case without delay. Then, the influence of delay on the dynamics of the system is investigated using the geometric criterion developed by Beretta and Kuang. 26 We show that the positive steady state can be destabilized through a Hopf bifurcation and there exist stability switches under some conditions. The formulas determining the direction and the stability of Hopf bifurcations are explicitly derived by using the center manifold reduction and normal form theory. Finally, some numerical simulations are performed to illustrate and expand our theoretical results.     

Dynamical behaviors of a prey-predator system with impulsive control

In this paper, we study dynamics of a prey-predator system under the impulsive control. Sufficient conditions of the existence and the stability of semi-trivial periodic solutions are obtained by using the analogue of the Poincaré criterion. It is shown that the positive periodic solution bifurcates from the semi-trivial periodic solution through a transcritical bifurcation. A strategy of impulsive state feedback control is suggested to ensure the persistence of two species. Furthermore, a steady positive period-2 solution bifurcates from the positive periodic solution by the flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations. Numerical simulations are also illustrated which agree well with our theoretical analysis.     

New explicit critical criterion of Hopf–Hopf bifurcation in a general discrete time system

Hopf–Hopf bifurcation is one of typical codimension-two bifurcations, which requires some rigid bifurcation conditions and occurs only in high-dimension systems. In this paper, a new critical criterion of this bifurcation is presented for a general discrete time system. Unlike the corresponding classical critical criterion (or the bifurcation definition), the new criterion is composed of a series of algebraic conditions explicitly expressed by the coefficients of the characteristic polynomial, which does not depend on eigenvalue computations of Jacobian matrix. This characteristic gives the advantage of the proposed criterion which is more convenient and efficient for detecting the existence of this type of codimension-two bifurcation or exploring the parameter mechanism of the bifurcation than the corresponding classical criterion. The equivalence between the proposed criterion and the corresponding classical criterion is rigorously proved. The bifurcation design problem of a three-degree-of-freedom vibro-impact system is used as example to show the effectiveness of the proposed criterion.     

Dynamics of a Delayed Predator-prey System with Stage Structure for Predator and Prey

In this paper, a predator-prey system with two discrete delays and stage structure for both the predator and the prey is investigated. The dynamical behaviors such as local stability and local Hopf bifurcation are analyzed by regarding the possible combinations of the two delays as bifurcating parameter. Some explicit formulae determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form method and the center manifold theory. Finally, numerical simulations are presented to support the theoretical analysis.     

Iterative solvers and inflow boundary conditions for plane sudden expansion flows

Incompressible laminar flow in a symmetric plane sudden expansion is studied numerically. The flow is known to exhibit a stable symmetric solution up to a critical Reynolds number above which symmetry-breaking bifurcation occurs. The aim of the present study is to investigate the effect of using different iterative solvers on the calculation of the bifurcation point. For this purpose, the governing equations for steady two-dimensional incompressible flow are written in terms of a stream function-vorticity formulation. A second order finite volume discretization is applied. Explicit and implicit solvers are used to solve the resulting system of algebraic equations. It is shown that the explicit solver recovers the stable asymmetric solution, while the implicit solver can recover both the unstable symmetric solution or the stable asymmetric solution, depending on whether the initial guess is symmetric or not. It is also found that the type of inflow velocity profile, whether uniform or parabolic, has a significant effect on the onset of bifurcation as uniform inflows tend to stabilize the symmetric solution by delaying the onset of bifurcation to a higher Reynolds number as compared to parabolic inflows.     

Anti-Controlling Codimension-2 Bifurcation of Discrete Dynamical Systems in 1 : 2 Resonance北大核心CSCD

从分岔反控制的角度设计了一套非线性反馈控制策略,来实现离散动力系统1∶2共振情形下余维二分岔的各种分岔解。首先,针对传统分岔准则在确定高余维分岔点时存在的局限性,建立了一个1∶2共振情形下的余维二分岔的新显式准则,基于这个显式准则通过设计线性控制增益来确保此类余维二分岔的存在性。然后,推导了1∶2共振的中心流形,并基于范式方法通过设计非线性控制增益,分析了1∶2共振情形下余维二分岔解的类型和稳定性。最后,以一个Arneodo-Coullet-Tresser映射为例,在指定的参数点处通过控制实现了具有1∶2共振分岔特性的各种分岔解,进一步验证了理论分析。     

Hopf bifurcation of the third-order Hénon system based on an explicit criterion

In this paper, Hopf bifurcation of the third-order Hénon system is studied via a simple explicit criterion, which is derived from the Schur–Cohn Criterion. Moreover stability of Hopf bifurcation is also investigated by using the normal form method and center manifold theory for the discrete time system developed by Kuznetsov. Test results containing simulations and circuit measurement are shown to demonstrate that the criterion is correct and feasible.