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We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.

We investigate the dynamical phase transition of two-component Bose-Einstein condensate with nonlinear tunneling, which is trapped inside a double-well and dispersively coupled to a single mode of a high-finesse optical cavity with one moving end mirror driven by a single mode standing field. The nonlinear tunneling interaction leads to an increase of stability points and riches the phase diagram of the system. It is shown that the appearance of the moving end mirror speeds up the tunneling of Bose-Einstein condensates, which makes population difference between two wells and regulates the number of the stability points of the system., Comment: 9 pages, 7 figures

Gallenene, an analogue of graphene composed of gallium, is epitaxially grown on Si(1 1 1) surface and studied by low temperature scanning tunneling microscopy (LT-STM). The STM images display that the buffer layer has a superstructure with respect to the substrate lattice and the gallenene layer has a hexagonal honeycomb structure. The scanning tunneling spectra (STS) of the gallenene show that it behaves as a metallic layer. First-principles calculations give the proposed configuration. Our results provide a method to synthesize the gallenene and shed important light on the growth mechanism of it.

The interaction functions of electrically coupled Hindmarsh–Rose (HR) neurons for different firing patterns are investigated in this paper. By applying the phase reduction technique, the phase response curve (PRC) of the spiking neuron and burst phase response curve (BPRC) of the bursting neuron are derived. Then the interaction function of two coupled neurons can be calculated numerically according to the PRC (or BPRC) and the voltage time course of the neurons. Results show that the BPRC is more and more complicated with the increase of the spike number within a burst, and the curve of the interaction function oscillates more and more frequently with it. However, two certain things are unchanged: = 0, which corresponds to the in-phase synchronization state, is always the stable equilibrium, while the anti-phase synchronization state with = 0.5 is an unstable equilibrium.

Three different methods are used to manipulate and control phthalocyanine based single molecular rotors on Au (111) surface: (1) changing the molecular structure to alter the rotation potential; (2) using the tunnelling current of the scanning tunnelling microscope (STM) to change the thermal equilibrium of the molecular rotor; (3) artificial manipulation of the molecular rotor to switch the rotation on or off by an STM tip. Furthermore, a molecular 'gear wheel' is successfully achieved with two neighbouring molecules.

The spatiotemporal order and rhythm dynamics of a complex neuronal network with mixed bursting neurons are studied in this paper. A quantitative characteristic, the width factor, is introduced to describe the rhythm dynamics of an individual neuron, and the average width factor is used to characterize the rhythm dynamics of a neuronal network. An r parameter is introduced to denote the ratio of the short bursting neurons in the network. Then we investigate the effect of the ratio on the rhythm dynamics of the neuronal network. The critical value of r is derived, and the neurons in the network always remain short bursting when the r ratio is larger than the critical value.

We investigate synchronization of Hindmarsh—Rose neurons with gap junctions under the control of a pacemaker. In a ring Hindmarsh—Rose neuronal network, the coupled neurons with the pacemaker can occur in synchronization more easily than those without the pacemaker. Furthermore, the pacemaker can induce phase synchronization or nearly-complete synchronization of nonidentical neurons. This synchronization can occur more easily when time delay is considered. Theses results can be helpful to understand the activities of the real neuronal system.