共查询到17条相似文献,搜索用时 236 毫秒
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从构造驱动系统和响应系统之间的函数关系出发,一般性地研究了广义混沌同步中同步流形的多值性问题,并对同步流形的稳定性进行了分析,提出了多稳定同步流形存在的条件.利用该稳定性条件对两个实例进行了分析,一个为Genesio-Rssler耦合系统,另一个为具有二次、三次非线性的耦合Duffing系统,结果表明前者仅有唯一的稳定同步流形,而后者随着耦合强度的增加,从具有两个稳定的同步流形变为只存在一个稳定同步流形.
关键词:
混沌同步
多稳定性
同步流形 相似文献
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运用广义胞映射图方法研究两个周期激励作用下Duffing-van der Pol系统的全局特性.发现了系统的混沌瞬态以及两种不同形式的瞬态边界激变, 揭示了吸引域和边界不连续变化的原因. 瞬态边界激变是由吸引域内部或边界上的混沌鞍和分形边界上周期鞍的稳定流形碰撞产生.第一种瞬态边界激变导致吸引域突然变小, 吸引域边界突然变大; 第二种瞬态边界激变使两个不同的吸引域边界合并成一体.此外, 在瞬态合并激变中两个混沌鞍发生合并, 最后系统的混沌瞬态在内部激变中消失. 这些广义激变现象对混沌瞬态的研究具有重要意义.
关键词:
广义胞映射图方法
Duffing-van der Pol
混沌瞬态
广义激变 相似文献
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对单向耦合下两个不同的Lorenz系统的广义同步进行了研究,利用辅助系统方法,基于稳定性理论和响应系统的有界性,得到了它们达到广义同步时的充分条件,并根据响应系统的修正系统具有零渐近稳定平衡点、非零渐近稳定平衡点和轨道渐近稳定周期解的情况,将广义同步分为第一类、第二类和第三类;利用Routh-Hurwitz定理,对修正系统平衡点的稳定性进行了分析,给出了单向耦合下两个不同Lorenz系统具有第一类、第二类广义同步的充分条件.数值仿真表明了该方法的有效性与可行性. 相似文献
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研究了两个耦合格子动力系统的非线性相互作用。当两个耦合格子系统一样时,则导致完全同步化。而当两个耦合格子系统的参数不一样或者这两个系统不相同时,则导致广义同步化。计算了Lyapunov指数谱。 相似文献
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Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems 下载免费PDF全文
The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.%vspace1mm 相似文献
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In this paper, with a given manifold y= H(x) , we have constructed
a response system for a continuous-time chaotic system as a drive
system, and used impulsive control theory to demonstrate
theoretically that this response system can achieve impulsive
generalized synchronization (GS) with the drive system. Our
theoretical result is supported by numerical examples. 相似文献
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Zheng Zhi-gang Feng Xiao-qin Ao Bin Michael C. Cross 《Frontiers of Physics in China》2006,1(4):458-467
In this paper, partial synchronization (PaS) in networks of coupled chaotic oscillator systems and synchronization in sparsely
coupled spatiotemporal systems are explored. For the PaS, we reveal that the existence of PaS patterns depends on the symmetry
property of the network topology, while the emergence of the PaS pattern depends crucially on the stability of the corresponding
solution. An analytical criterion in judging the stability of PaS state on a given network are proposed in terms of a comparison
between the Lyapunov exponent spectrum of the PaS manifold and that of the transversal manifold. The competition and selections
of the PaS patterns induced by the presence of multiple topological symmetries of the network are studied in terms of the
criterion. The phase diagram in distinguishing the synchronous and the asynchronous states is given. The criterion in judging
PaS is further applied to the study of synchronization of two sparsely coupled spatiotemporal chaotic systems. Different synchronization
regimes are distinguished. The present study reveals the intrinsic collective bifurcation of coupled dynamical systems prior
to the emergence of global synchronization. 相似文献
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Realization of generalized synchronization between different chaotic systems via scalar controller 下载免费PDF全文
In this paper, a very simple generalized synchronization method between
different chaotic systems is presented. Only a scalar controller is used in
this method. The method of obtaining the scalar controller from chaotic
systems is established. The sufficient and necessary condition of
generalized synchronization is obtained from a rigorous theory,
and the
sufficient and necessary condition of generalized synchronization is
irrelative to chaotic system itself. Theoretical analyses
and simulation results
show that the method established in this paper is effective. 相似文献
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采用扩阶方法(使响应系统和驱动系统的维数相同),把不同阶数混沌系统的广义同步问题转化为相同阶数混沌系统之间的广义同步,基于Lyapunov稳定性定理和自适应控制方法(用于相同阶数混沌系统的同步),给出了自适应控制器和参数自适应律,进而实现了不同阶数混沌系统的广义同步.将该方法应用于参数未知的超Lü,Lorenz,广义Lorenz和Liu等系统之间的广义混沌同步,理论证明了该方法可以使这些系统达到渐近广义同步,并且可以辨识驱动系统和响应系统的所有参数,数值模拟进一步证明了该方法的有效性. 相似文献
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In this paper, generalized synchronization of two
different chaotic dynamical systems is investigated. An active control is
adopted to construct a response system which synchronizes with a given drive
system for a function relation. Based on rigorous analysis, the error system
is asymptotically stable at the equilibrium. Numerical simulations
illustrate the effectiveness of the proposed theory. 相似文献
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In this paper, using scalar feedback controller and stability theory of
fractional-order systems, a generalized synchronization method for different
fractional-order chaotic systems is established. Simulation results show the
effectiveness of the theoretical results. 相似文献