共查询到18条相似文献,搜索用时 281 毫秒
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对应于混沌振子的各个Lyapunov指数,在切空间中定义了广义相位和广义旋转数.广义旋转数和Lyapunov指数相结合,可以更完整地描述混沌吸引子的各个运动模式的运动特征,包括伸缩与旋转.用耦合Duffing振子研究了时空混沌系统在同步混沌失稳时发生的分岔行为.结果表明,耦合振子的同步混沌态可以发生一种Hopf分岔,在Hopf分岔后,系统的功率谱中出现了一个特征频率,其值恰好等于分岔前临界横模的广义旋转数.
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本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程. 相似文献
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电流调制半导体激光器的混沌及其同步 总被引:6,自引:5,他引:1
研究了电流调制半导体激光器的混沌及其同步.通过数值计算系统的最大Lyapunov指数随调制强度的变化情况,确定了激光器处于混沌态的参量区间.利用差值耦合与和值耦合两种方案实现了两激光器的混沌同步.两激光器相关系数的数值计算表明,两种方案的同步效果都很好,而和值耦合更易于实现两激光器的同步.以标准化系数为例,分析了两激光器参量不匹配对混沌同步的影响,当标准化系数的偏差保持在小范围内时,两激光器仍可达到较好的同步,而差值耦合同步的鲁棒性优于和值耦合. 相似文献
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This paper constructs a new physical system, i.e., the fractional-order Rabinovich system, and investigates its stability, chaotic behaviors, chaotic control and matrix projective synchronization. Firstly, two Lemmas of the new system's stability at three equilibrium points are given and proved. Next, the largest Lyapunov exponent, the corresponding bifurcation diagram and the chaotic behaviors are studied. Then, the linear and nonlinear feedback controllers are designed to realize the system's local asymptotical stability and the global asymptotical stability, respectively. It's particularly significant that, the fractional matrix projective synchronization between two Rabinovich systems is achieved and two kinds of proofs are provided for Theorem 4.1. Especially, under certain degenerative conditions, the fractional matrix projective synchronization can be reduced to the complete synchronization, anti-synchronization, projective synchronization and modified projective synchronization of the fractional-order Rabinovich systems. Finally, all the theoretical analysis is verified by numerical simulation. 相似文献
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We consider a variant of two coupled Van der Pol oscillators with both attractive and repulsive mean-field interactions. In the presence of attractive coupling, the system is in the complete synchrony, while repulsive coupling shows anti-synchronization state leading to suppression of oscillations with increasing interaction strength. The coupled system with both attractive and repulsive interactions shows competitive tendencies of being complete synchronization and anti-synchronization resulting in the stabilization of the fixed point. We have also studied the effect of the damping coefficient of the VdP oscillator on the nature of the transition from oscillatory to a steady-state. These oscillators stabilize to unstable equilibrium point or coupling dependent inhomogeneous steady state via second or first-order transitions respectively depending upon the damping coefficient and coupling strength. These transitions are analyzed in the parameter plane by analytical and numerical studies of the two coupled Van der Pol oscillators. 相似文献
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Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points
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《中国物理 B》2021,30(10):100504-100504
The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively. However, the coupled oscillators in practice are nonidentical, and there exist mismatched parameters. It has been proved that under certain conditions, complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points, yet other cooperative behaviors are not addressed. In this paper, we further consider two coupled nonidentical oscillators with the same equilibrium points, where one oscillator is convergent while the other is chaotic,and explore their cooperative behaviors. We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings. In the case of directed coupling,death islands appear in two-parameter spaces. The mechanism inducing these transitions is presented. 相似文献
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We report experimental evidence of mixed synchronization in two unidirectionally coupled chaotic oscillators using a scalar coupling. In this synchronization regime, some of the state variables may be in complete synchronization while others may be in anti-synchronization state. We extended the theory by using an adaptive controller with an updating law based on Lyapunov function stability to include parameter fluctuation. Using the scheme, we implemented a cryptographic encoding for digital signal through parameter modulation. 相似文献
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The dynamics of indirectly coupled Lorenz circuits is investigated experimentally. The in-phase and anti-phase synchronization
of indirectly coupled chaotic oscillators reported in Phys. Rev.
E 81, 046216 (2010) is verified by physical experiments with electronic circuits. Two chaotic systems coupled through a common
dynamic environment shows the verity of synchronization behaviours such as anti-phase synchronization, in-phase synchronization,
identical synchronization, anti-synchronization, etc. 相似文献
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Controlling and synchronizing spatiotemporal chaos of the coupled Bragg acousto-optical bistable map system using nonlinear feedback 总被引:3,自引:0,他引:3
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In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required. 相似文献