Dynamic Self‐Assembly Adhesion of a Paraquat Droplet on a Pillar[5]arene Surface

The adhesion of herbicide droplets on leaf surfaces plays an important role in the herbicide's adsorption by crops. How to control the adhesive binding which occurs through dynamic self‐assembly between the macroscopic droplet and the surface is a challenging task. We introduce a host onto surfaces that controls the binding of guests in the paraquat droplets. The pillar[5]arene‐functional surface showed the selective binding of paraquat droplets via the host–guest interaction. The work is promising for improving the efficiency of herbicides.     

Choosing effective controlled nodes for scale-free network synchronization

Previous studies concerning pinning control of complex-network synchronization have very often demonstrated that in an unweighted symmetrical scale-free network, controlling the high-degree nodes is more efficient than controlling randomly chosen ones; due to the heterogeneity of the node-degree or edge-connection distribution of the scale-free network, small-degree nodes have relatively high probabilities of being chosen at random but their control has less influence on the other nodes through the network. This raises the question of whether or not controlling the high-degree nodes is always better than controlling the small ones in scale-free networks. Our answer to this is yes and no. In this study, we carry out extensive numerical simulations to show that in an unweighted symmetrical Barabasi-Albert scale-free network, when the portion of controlled nodes is relatively large, controlling the small nodes becomes better than controlling the big nodes and controlling randomly chosen nodes has approximately the same effect as controlling the big ones. However, we also show that for normalized weighted scale-free networks, controlling the big nodes is in fact always better than controlling the small ones.     

A general multiscroll Lorenz system family and its realization via digital signal processors

This paper proposes a general multiscroll Lorenz system family by introducing a novel parameterized nth-order polynomial transformation. Some basic dynamical behaviors of this general multiscroll Lorenz system family are then investigated, including bifurcations, maximum Lyapunov exponents, and parameters regions. Furthermore, the general multiscroll Lorenz attractors are physically verified by using digital signal processors.     

Using white noise to enhance synchronization of coupled chaotic systems

In the paper, complete synchronization of two chaotic oscillators via unidirectional coupling determined by white noise distribution is investigated. It is analytically proved that chaos synchronization could be achieved with probability one merely via white-noise-based coupling. The established theoretical result supports the observation of an interesting phenomenon that a certain kind of white noise could enhance chaos synchronization between two chaotic oscillators. Furthermore, numerical examples are provided to illustrate some possible applications of the theoretical result.     

Constructing a chaotic system with any number of equilibria

In the chaotic Lorenz system, Chen system and Rössler system, their equilibria are unstable and the number of the equilibria are no more than three. This paper shows how to construct some simple chaotic systems that can have any preassigned number of equilibria. First, a chaotic system with no equilibrium is presented and discussed. Then a methodology is presented by adding symmetry to a new chaotic system with only one stable equilibrium, to show that chaotic systems with any preassigned number of equilibria can be generated. By adjusting the only parameter in these systems, one can further control the stability of their equilibria. This result reveals an intrinsic relationship of the global dynamical behaviors with the number and stability of the equilibria of a chaotic system.     

Synchronized regions of pinned complex networks: spectral analysis

The synchronization problem for a complex dynamical network is investigated in this paper from a spectral analysis approach. It is assumed that only a small portion of the nodes in the network are chosen to be controlled, known as the pinning control scheme. Some new types of synchronized regions for networks with different node dynamics and inner-coupling structures are discovered, especially for the case of the special chaotic node systems with a stable equilibrium point under fully anti-diagonal and partially anti-diagonal couplings. The eigenvalue distributions of the coupling and control matrices for different types of complex networks are obtained. The effects of the network topology, global coupling strength, pinning density, and pinning strength on the network synchronizability are examined through extensive numerical simulations. It is shown that the synchronizability of the pinned network can be effectively improved by increasing the overall coupling strength, pinning density, and pinning strength for some classes of synchronized regions, whereas too large the pinning density and pinning strength will lead to desynchronization for other classes. It is found that small-world networks are not always easier to synchronize than regular rings, and a denser eigenvalue distribution may not always imply better synchronizability.     

Synchronization of a network coupled with complex-variable chaotic systems

In this paper, synchronization of a network coupled with complex-variable chaotic systems is investigated. Adaptive feedback control and intermittent control schemes are adopted for achieving adaptive synchronization and exponential synchronization, respectively. Several synchronization criteria are established. In these schemes, the outer coupling matrix is not necessarily assumed to be symmetric or irreducible. Further, for a class of networks with an irreducible and balanced outer coupling matrix, a pinning control scheme is adopted for achieving synchronization. Numerical simulations are demonstrated to verify the effectiveness of the theoretical results.     

Dynamics of Induced Maps on the Space of Probability Measures

Journal of Dynamics and Differential Equations - For a continuous self-map f on a compact metric space X, we provide two simple examples: the first confirms that shadowing of (X, f) is not...     

DC-DC buck变换器的分岔行为及混沌控制研究

研究了带负载电容的DC-DC buck变换器的分岔行为及其混沌控制问题，提到了一些新的有意义的结果.随着负载电容的增加，这种电路系统出现周期叠加序列窗口，且系统混沌运动的参数空间的测度逐渐趋于零，而且系统处在周期运动区时其电压转换效率高于系统处在混沌运动区时的电压转换效率，这些结果对于实际电路的设计具有较好的参考价值.同时，采用外加周期脉冲控制方法，能有效地实现该电路系统中的混沌控制.     

Random walks on dual Sierpinski gaskets

We study an unbiased random walk on dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We first determine the mean first-passage time (MFPT) between a particular pair of nodes based on the connection between the MFPTs and the effective resistance. Then, by using the Laplacian spectra, we evaluate analytically the global MFPT (GMFPT), i.e., MFPT between two nodes averaged over all node pairs. Concerning these two quantities, we obtain explicit solutions and show how they vary with the number of network nodes. Finally, we relate our results for the case of d = 2 to the well-known Hanoi Towers problem.