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     

赤潮藻类生态营养模型非线性动力研究

基于营养盐、赤潮藻类、植食浮游动物之间的食物链关系,考虑到由于海洋内微生物分解动植物遗体对营养盐的补充以及物理因素导致的流失,文中建立了营养盐一赤潮藻类一植食性浮游动物相互作用的耦合生态动力学模型。运用现代非线性动力学理论,对模型解的动力学稳定性进行了分析。结果表明,随着参数的变化,系统稳定性也随之变化,甚至出现HOPF分岔现象。     

海洋生态非线性动力学模型的随机Hopf分岔

根据藻类-浮游动物的食物链关系,建立了一个随机非线性动力学模型,运用随机平均法对模型进行了化简,运用拟不可积Hamilton系统的相关理论和Oseledec乘性遍历定理求解了模型的最大Lyapunov指数,得到了模型随机稳定性的条件;利用动态系统不变测度的Lyapunov指数和系统响应概率密度并结合奇异边界的性态分析了模型的随机Hopf分岔行为,得到了分岔参数,并讨论了分岔参数对系统性态的影响.     

一个单种P-Z赤潮生态模型的非线性分析

对植食性浮游动物摄食模型(仅对一个赤潮藻类)进行非线性分析,得出了该确定性参数方程的稳定性条件和发生 Hopf 分岔的条件,并且用数值模拟证实了理论分析.为更好的吻合实际情况,提出了含有变参数的赤潮藻类生长模型.模型中用一个周期函数来近似模拟了藻类生长率参数,并对此模型做了数值模拟.结果表明,引入变参数后的模型能出现概周期解,更能体现藻类生长的季节性特点,与实际情况符合更好.     

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。     

赤潮藻类营养盐限制方程的非线性动力学研究

以赤潮代表性藻类－硅藻为研究对象，利用生物生长的生化机理，并考虑在海洋富营养化条件下氮和磷的浓度变化对藻类生长的影响及底物消耗和反馈机制，建立了新的藻类生长非线性动力学模型。首次利用现代非线性动力学的方法，研究了其解析解的分岔行为。指出了磷是影响藻类生长的限制营养盐因子，并对模型进行了仿真。文章对赤潮发生的预警和预测有一定的参考价值。     

赤潮藻类非线性动力学模型的随机分岔

选取典型赤潮藻类的硅藻和甲藻,建立了一个随机非线性动力学模型,运用随机平均法结合现代非线性动力学理论对模型进行了化简,运用拟不可积 Hamilton 系统的相关理论和 Oseledec 乘性遍历定理求解了模型的最大 Lyapunov 指数,得到了模型随机稳定性的条件;利用动态系统不变测度的 Lyapunov 指数分析了模型的随机分岔,得到了系统发生随机D-分岔时参数的取值条件,结果表明,系统在随机因素作用下变得更敏感、更不稳定.     

海洋生态系统非线性动力学研究

海洋生态经济系统非线性动力学模型的建立及分析,对我国海洋生态经济发展乃至社会经济的发展都具有重要意义.建立了新的海洋生态经济系统动力学模型,研究了模型的稳定性和分岔现象,揭示了该系统的非线性动力学特性.     

胶州湾北部水层生态动力学模型与模拟 Ⅱ.胶州湾北部水层生态动力学的模拟研究

利用建立起的浅海水层生态动力学箱式模型,模拟了胶州湾北部１９９５年的浮游植物、浮游动物、无机氮、无机磷、溶解氧以及ＤＯＣ和ＰＯＣ年变化特征。结果是合理的。通过模型参数敏感性实验分析,揭示了该模型系统的一些动力学特征     

南麂列岛附近海域浮游动物的分布及其与浮游藻类和营养盐的关系

本文描述了南麂列岛附近海域浮游动物的分布及其与浮游藻类和营养盐之间的关系。结果显示：浮游动物丰度与浮游藻类细胞总密度和硅藻细胞密度有正相关性,与硅酸盐和硝酸盐的浓度有负相关性。     

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。     

变参数赤潮藻类生长模型的非线性动力分析研究

在对一个营养盐和赤潮藻类摄食模型进行非线性分析的基础上,提出了含有变参数的赤潮藻类生长模型。模型中用一个周期阶跃函数来近似模拟了藻类生长率参数,并对此模型做了数值模拟。结果表明,引入变参数后的模型更能体现藻类生长的季节性特点,和实际情况符合更好。     

结构与尾流非线性耦合涡激振动预测模型

预测圆柱涡激振动的尾流振子模型中,通常采用线性的耦合模型,例如位移或者速度、加速度耦合来表征结构对尾流的作用。三种线性模型在预测圆柱锁频阶段的动力特性时存在差异,而且适用范围也受质量比的限制。提出了考虑结构与尾流动力非线性耦合的模型,该模型基于加速度耦合并结合速度耦合进行修正,适用范围不受质量比的影响;与实验结果的对比表明该模型可以更合理地给出锁频区域以及结构位移响应和尾流升力。最后,利用新模型讨论了质量比对锁频阶段结构振动幅值、尾流升力及频率比的影响;结果表明,随着质量比的增大,结构锁频区域变窄,结构振幅和尾流升力幅值减小。     

Maximum run-up,breaking conditions and dynamical forces in the swash zone: a boundary value approach

On the basis of the approximate analytical solution for the nonlinear shallow water equations of Antuono and Brocchini [M. Antuono & M. Brocchini, The boundary value problem for the nonlinear shallow water equation, Stud. Appl. Maths, 119, 71–91 (2007).], we propose useful regression curves for the prediction of maximum run-up and dynamical forces in the swash zone on a frictionless, uniformly sloping beach. For the first time the dependence of the results on both the wave height and the wave steepness is analyzed in detail providing formulae able to describe a wide class of wave inputs. Finally, the regression formulae are validated through comparison with maximum run-up laws and breaking conditions already available in the literature, the present model results appearing to better account for nonlinear effects.     

Applying chaos to radar detection in an ocean environment: anexperimental study

Ship navigation through ice-infested waters is a problem of deep concern to the oil exploration industry of Northern countries. Conventional marine radars do not perform satisfactorily in detecting small targets such as small pieces of iceberg. This paper reports a new method for detection in an ocean environment. The approach is based on the recent observation that sea clutter, radar echoes from the sea surface, can be modeled as a nonlinear deterministic dynamical system which can be used as an alternative to the conventional stochastic process. Based on this model, detection in sea clutter is considered as dynamical system classification instead of statistical hypothesis testing. Two dynamical detection methods are proposed. The first one uses a dynamical invariant called the attractor dimension to distinguish a target from a pure clutter process. The second approach tries to detect the existence of a target by observing the “difference” of the motion of the target and the clutter process. To show the validity of the idea of dynamical detection in sea clutter, real sea clutter, and target data were used in this study     

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.     

The retrieval of the nonlinear random waves from the non-Gaussian characteristics of the sea surface elevation distribution

In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.     

基于空间基函数客观拟合的副高突变与多态机理分析

为分析研究副热带高压异常活动的动力学机理,基于热力强迫和涡动耗散效应的大气偏微涡度方程,采用Galerkin方法进行方程的时-空变量分离,针对常规方法在空间基函数选择中存在的不足和欠缺,提出了从实际资料场序列中用经验正交函数(EOF)分解与遗传算法结合客观反演空间基函数的研究思想.通过对副热带高压位势场逐日时间序列的EOF分解,选择累积方差贡献超过90%的前3个主要空间典型场作为拟合对象,随后选择一组三角函数簇作为广义空间基函数,以该基函数与EOF典型场的误差最小二乘和基函数间的完备正交性构造双约束泛函,     

Dynamic Modeling and Three-Dimensional Motion Analysis of Underwater Gliders

For Cconsideration ofing both the eccentric rotatable rigid body and the translational rigid body, the dynamic model of the underwater glider is derived. Dynamical behaviors are also studied based on the model and can be used as the guidance to underwater gliders design. Gibbs function of the underwater glider system is derived first, and then the nonlinear dynamic model is obtained by use of Apell Equations. The relationships between dynamical behaviors and design parameters are studied by solving the dynamic model. The spiral motion, swerving motion in three dimensions and the saw-tooth motion of the underwater glider in vertical plane are studied. Lake trials are carried out to validate the dynamic model.