Phase—Locking in Coupled Chaotic Oscillators

The transition from the phase-unlocking state to the phase-locking state is found at the desynchronization of synchronous chaos of coupled oscillators.In the phase-locking case,the motions of all oscillators are chaotic and desynchronized,however spatial ordering is identified in their phase distribution.     

Synchronization of Coupled Oscillators on Newman-Watts Small-World Networks

We investigate the collection behaviour of coupled phase oscillators on Newman-Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with the others following the Kuramoto model We then study the onset of global synchronization of phases and frequencies based on dynamic simulations and finite-size scaling. Both the phase and frequency synchronization are observed to emerge in the presence of a tiny fraction of shortcuts and enhanced with the increases of nearest neighbours and lattice dimensions.     

Robust adaptive synchronization of chaotic neural networks by slide technique

In this paper, we focus on the robust adaptive synchronization between two coupled chaotic neural networks with all the parameters unknown and time-varying delay. In order to increase the robustness of the two coupled neural networks, the key idea is that a sliding-mode-type controller is employed. Moreover, without the estimate values of the network unknown parameters taken as an updating object, a new updating object is introduced in the constructing of controller. Using the proposed controller, without any requirements for the boundedness, monotonicity and differentiability of activation functions, and symmetry of connections, the two coupled chaotic neural networks can achieve global robust synchronization no matter what their initial states are. Finally, the numerical simulation validates the effectiveness and feasibility of the proposed technique.     

Gradient control and synchronization of Julia sets

This paper firstly introduces the control methods to fractals and give the definition of synchronization of Julia sets between two different systems. Especially, the gradient control method is taken on the classic Julia sets of complex quadratic polynomial Zn＋1 = zn^2＋ c, which realizes its Julia sets control and synchronization. The simulations illustrate the effectiveness of the method.     

SPATIO-TEMPORAL CHAOTIC SYNCHRONIZATION FOR MODES COUPLED TWO GINZBURG-LANDAU EQUATIONS

On the basis of numerical computation, the conditions of the modes coupling are proposed, and the high-frequency modes are coupled, but the low frequency modes are uncoupled. It is proved that there exist an absorbing set and a global finite dimensional attractor which is compact and connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations(MGLE). The trajectory of driver equation may be spatio-temporal chaotic. One associates with MGLE, a truncated form of the equations. The prepared equations persist in long time dynamical behavior of MGLE. MGLE possess the squeezing properties under some conditions. It is proved that the complete spatio-temporal chaotic synchronization for MGLE can occur. Synchronization phenomenon of infinite dimensional dynamical system (IFDDS) is illustrated on the mathematical theory qualitatively. The method is different from Liapunov function methods and approximate linear methods.     

Enhanced Synchronization of Intercellular Calcium Oscillations by Noise Contaminated Signals

We consider the dynamics of locally coupled calcium oscillation systems, each cell is subjected to extracellular contaminated signal, which contains common sub-threshold signal and independent Gaussian noise. It is found that intermediate noise can enhance synchronized oscillations of calcium ions, where the frequency of noise-induced oscillations is matched with the one of sub-threshold external signal. We show that synchronization is enhanced as a result of the entrainment of external signal. Furthermore, the effect of coupling strength is considered. We find above-mentioned phenomenon exists only when coupling strength is very small. Our findings may exhibit that noise can enhance the detection of feeble external signal through the mechanism of synchronization of intercellular calcium ions.     

Synchronization in Coupled Oscillators with Two Coexisting Attractors

Dynamics in coupled Dufling oscillators with two coexisting symmetrical attractors is investigated. For a pair of Dufl~ng oscillators coupled linearly, the transition to the synchronization generally consists of two steps： Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions.     

Synchronization and Pattern Dynamics of Coupled Chaotic Maps on Complex Networks

The synchronization and pattern dynamics of coupled logistic maps on a certain type of complex network, constructed by adding random shortcuts to a regular ring, is investigated. For parameters where an isolated map is fully chaotic, the defect turbulence, which is dominant in the regular network, can be tamed into ordered periodic patterns or synchronized chaotic states when random shortcuts are added, and the patterns formed on the complex network can be grouped into two or three branches depending on the coupling strength.     

关于非线性系统两类广义混沌同步存在性的研究

研究了非线性系统两类广义混沌同步的存在性.即在响应系统的修正方程在具有渐近稳定平衡点或渐近稳定周期轨道的情况下,满足一定的条件,可将广义同步化流形存在性问题转化为Lipschitz函数族的压缩不动点问题,理论上严格证明了该广义同步化流形的指数吸引性.数值仿真证实了理论的正确性及有效性. 关键词： 广义同步化流形 压缩不动点 指数吸引性     

关于非自治系统三类广义同步存在性的研究

研究了两个单向耦合的非自治系统三类广义同步的存在性.在响应系统的修正方程具有渐近稳定平衡点、渐近稳定周期轨道或渐近稳定拟周期轨道的情况下,满足一定的条件,可将广义同步化流形存在性问题转化为Lipschitz函数族的压缩不动点问题,并且理论证明了该广义同步化流形的指数吸引性.同时,以Duffing系统为例进行了数值仿真,其结果与理论推导相一致. 关键词： 广义同步化流形 压缩不动点 指数吸引性