共查询到20条相似文献,搜索用时 138 毫秒
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本文从理论上讨论了低纬度大气、海洋耦合系统中多年振荡的现象。文中采用一个沿纬圈平均的二维模式,其中大气部分是斜压的,海洋部分包括混合层和温跃层,通过海洋大气间动力和热力的相互作用耦合起来。分析结果表明,系统中发展着一类周期为三年左右的自由振荡,从而证实了这个大尺度海气相互作用中一个重要的观测事实。 相似文献
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一类平面七次多项式系统赤道环的稳定性与极限环分支 总被引:2,自引:0,他引:2
本文研究一类平面七次多项式系统赤道环的稳定性和极限环分支,给出了系统的前12个奇点量公式,可积性条件及在赤道附近存在3个极限环的条件,较为精细地指出了极限环的存在位置。 相似文献
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林振山 《数学物理学报(A辑)》2003,23(1):60-64
该文对海气耦合双变量随机气候模式进行了系统研究,研究结果表明:(1)无论是考虑只有大气子系统的随机作用还是同时考虑大气子系统和海洋子系统的双扰动,对给定的扰动频率,海气气候系统对大气的扰动作用相当于一个十分简单的线性放大器;对于不同的扰动频率,在能量上海温的变化将随大气的扰动做4次幂的非线性响应;(2)若同时考虑大气子系统和海洋子系统的随机扰动,在满足细致平衡条件下可以求出系统定态的概率分布。否则,只有当扰动为弱噪声时,才能用级数展开法近似求出系统的概率分布。 相似文献
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沈伯骞 《数学年刊B辑(英文版)》1993,(6)
本文讨论了一类具有椭圆解的三次系统(E_3~2),证明了当椭圆解为此系统的极限环时,还可以存在其它极限环,并描绘出当具有椭圆极限环时此系统的所有可能的全局相图,此外,还举出了一个以此椭圆为无返回映射分界线环的例子,其内部包含三个奇点和至少一个极限环. 相似文献
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本文研究一类五次平面多项式系统赤道极限环分支问题.运用奇点量方法,首次证明了五次多项式系统可在赤道分支出十个极限环. 相似文献
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研究了一类七次系统无穷远点的中心条件与赤道极限环分支问题.通过将实系统转化为复系统研究,给出了计算无穷远点奇点量的递推公式,并在计算机上用Mathematica推导出该系统无穷远点前14个奇点量,进一步导出了无穷远点成为中心的条件和14阶细焦点的条件,在此基础上得到了七次系统无穷远点分支出12个极限环的一个实例. 相似文献
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沈伯骞 《数学年刊A辑(中文版)》1993,(6)
本文讨论了一类具有椭圆解的三次系统(E_3~2),证明了当椭圆解为此系统的极限环时,还可以存在其它极限环,并描绘出当具有椭圆极限环时此系统的所有可能的全局相图,此外,还举出了一个以此椭圆为无返回映射分界线环的例子,其内部包含三个奇点和至少一个极限环。 相似文献
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The Jin-Neelin model for the El Ni$\wt{\rm n}$o--Southern
Oscillation (ENSO for short) is considered for which the authors
establish existence and uniqueness of global solutions in time over
an unbounded channel domain. The result is proved for initial data
and forcing that are sufficiently small. The smallness conditions
involve in particular key physical parameters of the model such as
those that control the travel time of the equatorial waves and the
strength of feedback due to vertical-shear currents and upwelling;
central mechanisms in ENSO dynamics.
From the mathematical view point, the system appears as the coupling
of a linear shallow water system and a nonlinear heat equation.
Because of the very different nature of the two components of the
system, the authors find it convenient to prove the existence of
solution by semi-discretization in time and utilization of a
fractional step scheme. The main idea consists of handling the
coupling between the oceanic and temperature components by dividing
the time interval into small sub-intervals of length $k$ and on each
sub-interval to solve successively the oceanic component, using the
temperature $T$ calculated on the previous sub-interval, to then
solve the sea-surface temperature (SST for short) equation on the
current sub-interval. The passage to the limit as $k$ tends to zero
is ensured via a priori estimates derived under the aforementioned
smallness conditions. 相似文献
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Models for weather and climate prediction are complex, and each
model typi-cally has at least a small number of phenomena that are
poorly represented, such as perhaps the Madden-Julian Oscillation
(MJO for short) or El Ni\~{n}o-Southern Oscillation (ENSO for short)
or sea ice. Furthermore, it is often a very challenging task to
modify and improve a complex model without creating new
deficiencies. On the other hand, it is sometimes possible to design
a low-dimensional model for a particular phenomenon, such as the MJO
or ENSO, with significant skill, although the model may not
represent the dynamics of the full weather-climate system. Here a
strategy is proposed to mitigate these model errors by taking
advantage of each model''s strengths. The strategy involves
inter-model data assimilation, during a forecast simulation, whereby
models can exchange information in order to obtain more faithful
representations of the full weather-climate system. As an initial
investigation, the method is examined here using a simplified
scenario of linear models, involving a system of stochastic partial
differential equations (SPDEs for short) as an imperfect tropical
climate model and stochastic differential equations (SDEs for short)
as a low-dimensional model for the MJO. It is shown that the MJO
prediction skill of the imperfect climate model can be enhanced to
equal the predictive skill of the low-dimensional model. Such an
approach could provide a route to improving global model forecasts
in a minimally invasive way, with modifications to the prediction
system but without modifying the complex global physical model
itself. 相似文献
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Lev A. Smirnov Alexey K. Kryukov Grigory V. Osipov Jürgen Kurths 《Regular and Chaotic Dynamics》2016,21(7-8):849-861
The main goal of this research is to examine any peculiarities and special modes observed in the dynamics of a system of two nonlinearly coupled pendulums. In addition to steady states, an in-phase rotation limit cycle is proved to exist in the system with both damping and constant external force. This rotation mode is numerically shown to become unstable for certain values of the coupling strength. We also present an asymptotic theory developed for an infinitely small dissipation, which explains why the in-phase rotation limit cycle loses its stability. Boundaries of the instability domain mentioned above are found analytically. As a result of numerical studies, a whole range of the coupling parameter values is found for the case where the system has more than one rotation limit cycle. There exist not only a stable in-phase cycle, but also two out-of phase ones: a stable rotation limit cycle and an unstable one. Bistability of the limit periodic mode is, therefore, established for the system of two nonlinearly coupled pendulums. Bifurcations that lead to the appearance and disappearance of the out-ofphase limit regimes are discussed as well. 相似文献
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Based on neurophysiological evidence, theoretical studies have shown that walking can be generated by mutual entrainment of oscillations of a central pattern generator (CPG) and a body. However, it has also been shown that the time delay in the sensorimotor loop destabilizes mutual entrainment, and results in the failure to walk. Recently, it has been reported that if (a) the neuron model used to construct the CPG is replaced by physiologically faithful neuron model (Bonhoeffer–Van der Pol type) and (b) the mechanical impedance of the body (muscle viscoelasticity) is controlled depending on the angle between two legs, the phase relationship between CPG activity and body motion could be flexibly locked according to the loop delay and, therefore, mutual entrainment can be stabilized. That is, locomotor control adaptive to the loop delay can emerge from the coupling between CPG and body. Here, we call this mechanism flexible-phase locking. In this paper, we construct a system of coupled oscillators as a simplified model of a walking system to theoretically investigate the mechanism of flexible-phase locking, and to analyze the simplified model. The analysis suggests that the following are required as the essential mechanism: (i) an asymptotically stable limit cycle of the coupling system of CPG and body and (ii) a sign difference between afferent and efferent coupling coefficients. 相似文献
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To understand the competition between what are known as limit cycle and strange attractor dynamics, the classical oscillators that display such features were coupled and studied with and without external forcing. Numerical simulations show that, when the Duffing equation (the strange attractor prototype) forces the van der Pol oscillator (the limit cycle prototype), the limit cycle is destroyed. However, when the van der Pol oscillator is coupled to the Duffing equation as linear forcing, the two traditionally stable steady states are destabilized and a quasi-periodic orbit is born. In turn, this limit cycle is eventually destroyed because the coupling strength is increased and eventually gives way to strange attractor or chaotic dynamics. When two van der Pol oscillators are coupled in the absence of external periodic forcing, the system approaches a stable, nonzero steady state when the coupling strengths are both unity; trajectories approach a limit cycle if coupling strengths are equal and less than 1. Solutions grow unbounded if the coupling strengths are equal and greater than 1. Quasi-periodic solutions give way to chaos as the coupling strength increases and one oscillator is strongly coupled to the other. Finally, increasing the nonlinearity in both the oscillators is stabilizing whereas increasing the nonlinearity in a single oscillator results in subcritical instability. 相似文献
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在考虑成熟阶段具有密度制约的基础上,建立了一类具有卵-成熟阶段的同类相食模型.该文从两个方面讨论了模型的动力学性态:当种群不存在同类相食时,构造Lyapunov函数证明平衡点的全局渐近稳定性;当种群存在同类相食时,利用中心流形定理证明同类相食使模型产生鞍结点分支,通过构造Dulac函数说明在二维自治系统中不存在极限环,得到了平衡点的全局稳定性.最后,利用数值模拟验证了所得相应结果的正确性. 相似文献
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Creep groan of brake systems is a low frequency vibration phenomenon occurring at low speeds which can make passengers feel uncomfortable. This phenomenon is caused by the stick-slip-effect resulting in limit cycle oscillations with frequencies lower than 200 Hz. For the experimental investigation of this problem, an idealized brake test rig is designed concentrating on the investigation of the frictional contact by realizing low damping and small disturbances in the system. Different sensors are utilized in the test rig. Limit cycles and bifurcation effects can be observed in the experimental results. With respect to modeling, a one degree-of-freedom (DOF) model using Coulomb's friction law and a two DOF model using the bristle friction law are considered. In a comparative study of experimental and simulation results, the parameters of both friction laws can be identified from the dynamic experimental results, such as the static and dynamic friction coefficients, contact stiffness and Stribeck velocity. Experimental and theoretical results show a very good concordance. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Chieh-Li ChenChao Chung Peng Her-Terng Yau 《Communications in Nonlinear Science & Numerical Simulation》2012,17(4):1813-1823
A nonlinear system for controlling flutter in an aeroelastic system is proposed. The dynamic model describes the plunge and pitch motion of a wing. Interacting nonlinear forces such as structural and aerodynamic forces cause destabilizing phenomena such as flutter and limit cycle oscillation on the wing. Aeroelastic models have a wing section with only a single trailing-edge control surface for suppressing limit cycle oscillation. When modeling a single control surface, the controller design can achieve trajectory control of either plunge displacement or pitch angle, but not both, and internal dynamics describe the residual motion in closed-loop systems. Internal dynamics of aeroelasticity depend on model parameters such as freestream velocity and spring constant. Since single control surfaces have limited effectiveness, this study used leading- and trailing-edge control surfaces to improve control of limit-cycle oscillation. Moreover, two control surfaces were used to provide sufficient flexibility to shape both the plunge and the pitch responses. In this study, high order sliding mode control (HOSMC) with backstepping design achieved system stability and eliminated limit cycle phenomenon. Compared to the conventional sliding mode control design, the proposed control law not only preserves system robustness, but also avoids chatter phenomenon. Simulation results show that the proposed controller effectively regulate the response to origin in state space even under saturated controller input. 相似文献