共查询到19条相似文献,搜索用时 78 毫秒
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对于一类同时存在扩散耦合和梯度耦合的非线性振子系统, 通过空间傅里叶变换,得到具有不同波矢的各运动模式的相互独立的运动方程. 计算各横截模的Lyapunov指数, 可在耦合参数平面上确定同步混沌的稳定区域. 在稳定区域边界, 一对共轭横截模式失稳,导致同步混沌的Hopf分岔. 对耦合Lorenz振子系统进行了数值模拟,并设计了耦合Lorenz振子系统的电路, 进行耦合振子系统同步混沌Hopf分岔的电路仿真实验. 计算和仿真的结果表明,Hopf分岔的特征频率等于失稳横截模式的振荡频率.
关键词:
耦合非线性振子
同步混沌
横截模式
电路仿真 相似文献
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混沌系统的相同步现象是近几年混沌同步研究的热点,它反映了混沌运动中的有序行为.用分岔树来研究耦合系统相同步的进程,并用Lyapunov指数谱来探讨系统动力学在相同步时从高维混沌向低维混沌过渡的进程.发现了从多个有理同步的时间交替到完全相同步的道路.还 发现了相同步中的混沌抑制及通过倍周期分岔向混沌同步的恢复.此外,研究表明,非对称 耦合可以大大加强耦合系统的相同步,这对实际应用有重要的意义.
关键词:
相同步
分岔树
李指数 相似文献
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研究了一个时间混沌系统驱动多个时空混沌系统的并行同步问题.以单模激光Lorenz系统和一维耦合映像格子为例,在单模激光Lorenz系统中提取一个混沌序列,通过与一维耦合映像格子中的状态变量耦合使单模激光Lorenz系统和多个同结构一维耦合映像格子同时达到广义同步,并且多个一维耦合映像格子之间实现完全并行同步.通过计算条件Lyapunov指数,可以得到并行同步所需反馈系数的取值范围.数值模拟证明了此方法的可行性和有效性. 相似文献
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对改进恒Lyapunov指数谱混沌系统的广义投影同步进行了研究.用主动控制同步法设计合适的非线性反馈控制器,通过单向耦合,实现恒指数谱混沌系统的同结构广义投影同步与异结构广义投影同步.在指出广义投影同步体系中比例因子调节作用的同时,也分析了改进恒指数谱混沌系统的全局线性调幅参数对同步体系中两个系统的作用.基于模块与复用的设计思想,详细分析并构建了广义投影同步体系中的驱动系统、控制系统与响应系统.数值仿真与电路实验仿真一致显示:调节比例因子能够获得任意比例于原驱动混沌系统输出的混沌信号;调节全局线性调幅参数,能够同时线性调整同步体系中两个系统输出的状态变量的幅值,而不影响两个系统之间的广义投影同步.
关键词:
改进恒Lyapunov指数谱混沌系统
广义投影同步
比例因子
全局线性调幅参数 相似文献
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We investigate the Hopf bifurcation of the synchronous chaos in
coupled Lorenz oscillators. We find that the system undergoes a
phase transition along the Hopf instability of the synchronous
chaos. The phase transition makes the traveling wave component
with the phase difference φ(i)-φ(i+1)=2π/N between
adjacent sites unstable. The phase transition also plays a role to
relate the Hopf bifurcation with the co-dimension two bifurcation
of the synchronous chaos. 相似文献
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The dynamic behavior of coupled chaotic oscillators is investigated. For small coupling, chaotic state undergoes a transition from a spatially disordered phase to an ordered phase with an orientation symmetry breaking. For large coupling, a transition from full synchronization to partial synchronization with translation symmetry breaking is observed. Two bifurcation branches, one in-phase branch starting from synchronous chaos and the other antiphase branch bifurcated from spatially random chaos, are identified by varying coupling strength epsilon. Hysteresis, bistability, and first-order transitions between these two branches are observed. 相似文献
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Spatiotemporal symmetry in rings of coupled biological oscillators of Physarum plasmodial slime mold
Spatiotemporal patterns in rings of coupled biological oscillators of the plasmodial slime mold, Physarum polycephalum, were investigated by comparing with results analyzed by the symmetric Hopf bifurcation theory based on group theory. In three-, four-, and five-oscillator systems, all types of oscillation modes predicted by the theory were observed including a novel oscillation mode, a half period oscillation, which has not been reported anywhere in practical systems. Our results support the effectiveness of the symmetric Hopf bifurcation theory in practical systems. 相似文献
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A nonautonomous nonlinear system is constructed and implemented as an experimental device. As represented by a 4D stroboscopic Poincaré map, the system exhibits a Smale-Williams-type strange attractor. The system consists of two coupled van der Pol oscillators whose frequencies differ by a factor of two. The corresponding Hopf bifurcation parameters slowly vary as periodic functions of time in antiphase with one another; i.e., excitation is alternately transferred between the oscillators. The mechanisms underlying the system’s chaotic dynamics and onset of chaos are qualitatively explained. A governing system of differential equations is formulated. The existence of a chaotic attractor is confirmed by numerical results. Hyperbolicity is verified numerically by performing a statistical analysis of the distribution of the angle between the stable and unstable subspaces of manifolds of the chaotic invariant set. Experimental results are in qualitative agreement with numerical predictions. 相似文献
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Direct time delay feedback can make non-chaotic Chen
circuit chaotic. The chaotic Chen circuit with direct time delay
feedback possesses rich and complex dynamical behaviours. To reach a
deep and clear understanding of the dynamics of such circuits
described by delay differential equations, Hopf bifurcation in the
circuit is analysed using the Hopf bifurcation theory and the
central manifold theorem in this paper. Bifurcation points and
bifurcation directions are derived in detail, which prove to be
consistent with the previous bifurcation diagram. Numerical
simulations and experimental results are given to verify the
theoretical analysis. Hopf bifurcation analysis can explain and
predict the periodical orbit (oscillation) in Chen circuit with
direct time delay feedback. Bifurcation boundaries are derived using
the Hopf bifurcation analysis, which will be helpful for determining
the parameters in the stabilisation of the originally chaotic
circuit. 相似文献
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John David Crawford 《Journal of statistical physics》1994,74(5-6):1047-1084
We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to obtain the amplitude equations for steady-state and Hopf bifurcation from the equilibrium state with a uniform phase distribution. When the population is described by a native frequency distribution that is reflection-symmetric about zero, the problem has circular symmetry. In the limit of zero extrinsic noise, although the critical eigenvalues are embedded in the continuous spectrum, the nonlinear coefficients in the amplitude equation remain finite, in contrast to the singular behavior found in similar instabilities described by the Vlasov-Poisson equation. For a bimodal reflection-symmetric distribution, both types of bifurcation are possible and they coincide at a codimension-two Takens-Bogdanov point. The steady-state bifurcation may be supercritical or subcritical and produces a time-independent synchronized state. The Hopf bifurcation produces both supercritical stable standing waves and supercritical unstable traveling waves. Previous work on the Hopf bifurcation in a bimodal population by Bonilla, Neu, and Spigler and by Okuda and Kuramoto predicted stable traveling waves and stable standing waves, respectively. A comparison to these previous calculations shows that the prediction of stable traveling waves results from a failure to include all unstable modes. 相似文献
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To date, there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity, due to the difficulties in theoretical analysis and numerical simulations. In this paper, we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us. We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of (13944.7021,13946.5333) by the method of bisection. Through Fourier analysis, it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval. Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram, Kolmogorov entropy and maximal Lyapunov exponent. The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic. 相似文献
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We investigate quantum-mechanical counterpart of a classical instability in a phase space by the numerical method of quantum
trajectories with moving basis. As an application the model of coupled two oscillators driven by a monochromatic force in
the presence of dissipation (intracavity second harmonic generation) is analyzed. The system of interest is characterized
by two bifurcations leading to ranges of instability: the Hopf bifurcation which connects a steady state dynamics of the oscillatory
modes to a self-pulsing temporal dynamics and the bifurcation of the period-doubling. The both two regimes are analyzed on
the framework of the semiclassical phase trajectories and the Wigner functions of the oscillatory modes in phase space. 相似文献
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This paper is concerned with the Hopf bifurcation control of a modified Pan-like chaotic system. Based on the Routh-Hurwtiz theory and high-dimensional Hopf bifurcation theory, the existence and stability of the Hopf bifurcation depending on selected values of the system parameters are studied. The region of the stability for the Hopf bifurcation is investigated.By the hybrid control method, a nonlinear controller is designed for changing the Hopf bifurcation point and expanding the range of the stability. Discussions show that with the change of parameters of the controller, the Hopf bifurcation emerges at an expected location with predicted properties and the range of the Hopf bifurcation stability is expanded. Finally,numerical simulation is provided to confirm the analytic results. 相似文献