共查询到20条相似文献，搜索用时 93 毫秒
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研究微分方程定性理论的应用，利用定性分析的方法，讨论了一类在生化反应中的动力系统，证明了其极限环的存在性、不存在性及极限环的存在唯一性，从而得到了完整的结果。 相似文献
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渤海赤潮藻类生态动力学模型的非线性动力学研究 总被引：11，自引：3，他引：11
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 相似文献
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《中国海洋大学学报(自然科学版)》2016,(3)
应用Lyapunov函数分解法(即标量和的Lyapunov函数法),结合微分方程与微分差分方程的等价性的方法(即分解等价法),研究了具有大时滞的非线性定常大系统的无条件稳定性,得到了该系统为无条件稳定的充分性判据。本文对时滞项的研究不同于以往的小时滞,找到了使含大时滞项的系统为无条件稳定的途径,从而为这类问题的研究给出了一种新方法。 相似文献
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梁体在火作用下的响应取决于许多因素,包括约束条件和梁体的性质.应用温度升高时钢材和混凝土的非线性应力-应变关系,基于能量守恒原理,建立有限差分平衡方程,在合理确定钢材和混凝土热工参数基础上,分别分析三面受火、一面受力的两端为固定铰支座钢梁和钢混凝土组合梁的响应,得到2种约束梁体在温度载荷作用下响应的异同点,为进一步研究火灾下钢梁和钢混凝土结构的力学性能和抗火极限提供参考. 相似文献
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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。 相似文献
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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. 相似文献
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Investigated in this study is the flow-induced vibration of a nonlinearly restrained curved pipe conveying fluid. The nonlinear equation of motion is derived by equilibrium of forces on microelement of the system under consideration. The spatial coordinate of the system is discretized by DQM (differential quadrature method). On the basis of the boundary conditions, the dynamic equation is solved by the Newton-Raphson iteration method. The numerical solutions reveal several complex dynamic motions for the variation of the fluid velocity parameter, such as limit cycle motion, buckling and so on. The result obtained also shows that the sub parameter regions corresponding to the several motions may change with the variation of some parameters of the curved pipe. The present study supplies a new reference for investigating the nonlinear dynamic response of some other structures. 相似文献
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应用Lyapunov等价法讨论了多滞后中立型非线性定常控制系统与不带滞后的线性定常控制系统的镇定问题.应用Lyapunov稳定性理论与Krosovskii最大最小特征值定理,得到了多滞后中立型非线性定常控制系统渐近稳定的结论,该结论是对前人结果的进一步扩展,并在非线性项的限制下给出了时滞的界限.最后,将上述结论推广到了多滞后中立型非线性时变控制系统. 相似文献
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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. 相似文献
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The nonlinear dynamic analysis of a multipoint slack moored buoy is performed under the action of first and second order wave forces. The nonlinearity of the system is caused by the geometric nonlinearity of the mooring lines. The resulting nonlinear equation of motion is solved by an incremental time marching scheme. The nonlinear responses of the system are analysed to investigate different kinds of dynamic instability phenomena that may arise due to the nonlinearity of the system. As an illustrative example, a hollow cylindrical buoy anchored to the sea bed by means of six slack mooring lines is considered. The responses of the system are obtained and analysed for three regular waves namely, 5 m/5 s, 12 m/10 s and 18 m/15 s. The results of the study show that different kinds of instability phenomena like nT subharmonic oscillations, symmetry breaking bifurcation and aperiodic responses may occur in slack mooring systems. Further, a second order wave force may considerably influence the dynamic stability of such systems. 相似文献
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研究了一类线性关联滞后广义大系统的变结构控制综合问题.首先根据系统的结构和控制输入的特定形式,引入了1种新的受限系统等价分解形式,把每个子系统分解成2个低维的动态子系统：1个是不带控制项的线性关联微分差分系统,另1个是带有控制项的线性关联差分系统.然后设计了带有积分动态补偿器的切换函数, 给出了滑动模渐近稳定的充分条件.最后设计了可以保证系统的解的轨迹到达切换流形的多层分散变结构控制.这种控制对物理上分散等类型的线性关联滞后广义系统是合理的有效的. 相似文献
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研究线性时滞系统的时滞相关稳定性问题。利用李雅普诺夫稳定性理论结合微分不等式 ,提出了若干个时滞相关稳定性的新判据 ,并给出了系统的时滞项上界的估计公式。得到的稳定性判据较简洁 ,且具有较低的保守性。 相似文献
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The purpose of this paper is to analyze the nonlinear ship roll motion equation and the main parameters that induce ship capsizing in beam seas, estimate the survival probability of a ferry in random seas and to find out a risk assessment method for the ship’s intact stability. A single degree of freedom (1-DOF) dynamic system of ship rolling in beam seas is investigated and the nonlinear differential equation is solved in the time domain by the fourth order Runge-Kutta algorithm. The survival probability of a ferry in beam seas is investigated using the theory of “safe basin”. The survival probability is calculated by estimating erosion of “safe basin” during ship rolling motion by Monte Carlo simulations. From the results it can be concluded that the survival probability of a ship in beam sea condition can be predicted by combining Monte Carlo simulations and the theory of “safe basin”. 相似文献
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针对水下系泊监测平台在水流涡激作用下的稳定性问题,考虑了浮体在振动过程中的变形,建立了其流固耦合的非线性动力学方程,利用谐波平衡法进行了非线性特性定性分析,Melnikov方法进行稳定性判据研究及影响因素分析,以系统出现混沌状态为稳定性控制条件,重点研究了系泊缆支撑间距对稳定性的影响,并计算出支撑间距的临界值。结果表明,系统稳定性随支撑间距增加而降低,当支撑间距超过临界值后,稍微增加都可能导致系泊监测平台振动偏离振动轨道而造成局部失稳甚至结构破坏。为保证监测平台的稳定性,应增加支撑数量,且支撑的间距不能超过系统发生失稳的临界值。 相似文献
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具有小时滞的线性系统次优控制的无滞后转换法 总被引：1，自引：0，他引：1
该文研究线性时滞定常系统的次优控制问题。根据无滞后转换法的思想 ,先引入状态向量的增量 ,将其视为附加扰动输入 ,再利用微分方程的逐次逼近法 ,将既含有时滞项又含有超前项的两点边值问题化为既不含时滞项又不含超前项的两点边值问题族。然后 ,把第 N次逼近得到的控制律近似为系统的最优控制律 ,得到次优控制律。并用实例仿真验证了该算法的有效性。该方法可使小时滞系统的迭代次数大大减少 ,因此尤其适合于小时滞系统的次优控制。 相似文献
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Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis. 相似文献