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将主动-被动同步法运用于离散混沌系统,对混沌同步问题进行了研究.根据Lyapunov稳定性理论,对系统进行一般分解,实现了离散系统的混沌同步,以Bragg声光双稳系统为例,验证了这种方法的有效性.仿真模拟结果表明,控制后的两个初始条件不同的Bragg声光双稳系统误差变量很快平稳地趋于零,说明这种同步方法是快速有效的.这种方法可以应用到任意的两个初始条件不同的离散和连续混沌系统,具有一定的普适性. 相似文献
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混沌运动对于一个经典的可积系统,存在着与系统自由数相等数目的运动积分。这样的系统在给定初始条件后,随时间的演变运动状态仅占据相空间的一部分,且通常具有周期性的特点,轨道分布在n 维环面上,不同的初始条件定义不同的环面,这样的运动是规则运动。另一方面,对规则运动,可以通过解运动方程给出运动的全部规律。 相似文献
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探讨了非周期力(有界噪声或混沌驱动力)在非线性动力系统混沌控制中的影响.以一类典型的含有五次非线性项的Duffing-van der Pol系统为范例,通过对系统的轨道、最大Lyapunov指数、功率谱幅值及Poincar截面的分析,发现适当幅值的有界噪声或混沌信号,一方面可以消除系统对初始条件的敏感依赖性,抑制系统的混沌行为,将系统的混沌吸引子转化为奇怪非混沌吸引子;另一方面也可以诱导系统的混沌行为,将系统的周期吸引子转化为混沌吸引子.从而揭示了非周期力在混沌控制中的双重功效:抑制混沌和诱导混沌.
关键词:
混沌控制
有界噪声
混沌驱动力 相似文献
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通过引入分布引力场,将混沌系统的同步问题等效为引力场中系统运行轨道一致问题,从而实现更多不同动力学混沌系统的同步.通过将混沌系统之间的耦合度定义为速度,因其与运动方程无关,从而有别于常见的混沌同步控制项,具有较强通用性.基于轨道逼近导出引力场中多个混沌系统同步的条件,给出同步轨道方程.数值仿真实验说明了该方法的有效性. 相似文献
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本文讨论了在不同初始条件下临界阻尼和过阻尼振动的位移—时间关系和相轨道,给出了质点在不同情况下趋于平衡所需要的时间与初始条件的关系,指出了一些教材中在这个问题论述上的局限与不足. 相似文献
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Chongsheng Cao Slim Ibrahim Kenji Nakanishi Edriss S. Titi 《Communications in Mathematical Physics》2015,337(2):473-482
In an earlier work we have shown the global (for all initial data and all time) well-posedness of strong solutions to the three-dimensional viscous primitive equations of large scale oceanic and atmospheric dynamics. In this paper we show that for certain class of initial data the corresponding smooth solutions of the inviscid (non-viscous) primitive equations, if they exist, they blow up in finite time. Specifically, we consider the three-dimensional inviscid primitive equations in a three-dimensional infinite horizontal channel, subject to periodic boundary conditions in the horizontal directions, and with no-normal flow boundary conditions on the solid, top and bottom boundaries. For certain class of initial data we reduce this system into the two-dimensional system of primitive equations in an infinite horizontal strip with the same type of boundary conditions; and then we show that for specific sub-class of initial data the corresponding smooth solutions of the reduced inviscid two-dimensional system develop singularities in finite time. 相似文献
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V.I. Yukalov 《Physics letters. A》2012,376(4):550-554
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A. V. Gurevich K. P. Zybkin G. A. Él’ 《Journal of Experimental and Theoretical Physics》1999,88(1):182-195
The behavior of the solution of the Korteweg-de Vries equation for large-scale oscillating periodic initial conditions prescribed
on the entire x axis is considered. It is shown that the structure of small-scale oscillations arising in a Korteweg-de Vries system as t→∞ loses its dynamical properties as a consequence of phase mixing. This process can be called the generation of soliton turbulence.
The infinite system of interacting solitons with random phases developing under these conditions leads to oscillations having
a stochastic character. Such a system can be described using the terms applied to a continuous random process, the probability
density and correlation function. It is shown that for this it suffices to determine from the prescribed initial conditions
amplitude distribution function of the solitons and their mean spatial density. The limiting stochastic characteristics of
the mixed state for problems with initial data in the form of an infinite sequence of isolated small-scale pulses are found.
Also, the problem of stochastic mixing under arbitrary initial conditions in the dispersionless limit (the Hopf equation)
is completely solved.
Zh. éksp. Teor. Fiz. 115, 333–360 (January 1999) 相似文献
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Based on the mean-field approximation, a system of nonlinear differential equations is obtained which describes the dynamics
of atomic-molecular conversion induced by two resonance Raman laser pulses. The obtained integrals of motion allow one to
reduce the problem to one evolution equation for the density of molecules. The solutions of this equation show that different
time evolution regimes of the system are possible, depending on the initial conditions: the periodic and aperiodic regimes
and the rest. The dependences of the period and amplitude on the initial density of particles and the initial phase difference
are studied in detail. The possibility of the phase control of the system dynamics is proved. 相似文献
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初值敏感性是混沌的本质,混沌的随机性来源于其对初始条件的高度敏感性,而Lyapunov指数又是这种初值敏感性的一种度量.本文的研究发现,混沌系统的级联可明显提高级联混沌的Lyapunov指数,改善其动力学特性.因此,本文研究了混沌系统的级联和级联混沌对动力学特性的影响,提出了混沌系统级联的定义及条件,从理论上证明了级联混沌的Lyapunov指数为各个级联子系统Lyapunov指数之和;适当的级联可增加系统参数、扩展混沌映射和满映射的参数区间,由此可提高混沌映射的初值敏感性和混沌伪随机序列的安全性.以Logistic映射、Cubic映射和Tent映射为例,研究了Logistic-Logistic级联、Logistic-Cubic级联和Logistic-Tent级联的动力学特性,验证了级联混沌动力学性能的改善.级联混沌可作为伪随机数发生器的随机信号源,用以产生初值敏感性更高、安全性更好的伪随机序列. 相似文献
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The conditions under which spin squeezing occurs in an asymmetric chain of spins are discussed. The time evolution of the system is calculated for different initial conditions. The effects of the use of spin coherent states to model the initial condition are analyzed. 相似文献
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利用耦合映像格子恢复信号初值是信号处理研究中一个重要的问题.耦合映像格子具有混沌系统的初值敏感性,当初值受到噪声污染时将会影响到系统对其的恢复.提出了一种由多个一维耦合映像格子系统并列耦合而成的多重耦合映像格子系统,通过将多个一维系统耦合,使因受到噪声干扰而趋向于指数分离的混沌轨道相互靠近,以达到抑制噪声的目的.数值仿真表明,该系统具有较强的抗噪声能力和较高的鲁棒性.在耦合系数选取适当的情况下,即使初始信号受到噪声干扰,该多重耦合系统仍然能够很好地恢复信号初值的统计特性,且对单个初值的恢复情况及与初始信号
关键词:
耦合映像格子
恢复信号的统计特性
多重耦合 相似文献
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Based on the Hamiltonian approach to an analysis of the system of Monod equations describing the chemostat dynamics, their
partial analytical solution is found for a certain class of initial conditions. It is shown that this class of initial conditions
can be easily realized in microbiological practice, and the solution obtained is generally described by the attractor of the
system trajectories. A methodical approach, which allows the given Hamiltonian formalism to be used to analyze the kinetics
of growth of microorganisms in the chemostat, is developed and experimentally checked.
Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–53, July, 2000. 相似文献