Fang Jin-Qing

Topological Properties and Transition Features Generated by a New Hybrid Preferential Model

A new hybrid preferential model (HPM) is proposed for generating both scale-free and small world properties. The topological transition features in the HPM from random preferential attachment to deterministic preferential attachment are investigated. It is found that the exponents γ of the power law are very sensitive to the hybrid ratio (d/r) of determination to random attachment, and γ increases as the ratio d/r increases. It is also found that there exists a threshold at d/r = 1/1, beyond which γ increases rapidly and can tend to infinity if there is no random preferential attachment (r = 0), which implies that the power law scaling disappears completely. Moreover, it is also found that when the ratio d/r increases, the average path length L is decreased, while the average clustering coefficient C is increased. Compared to the BA model and random graph, the new HPM has both the smallest L and the biggest C, which is consistent with most real-world growing networks.

Control of Beam Halo-Chaos for an Intense Charged-Particle Beam Propagating Through Double Periodic Focusing Field by Soliton

We study an intense beam propagating through the double periodic focusing channel by the particle-core model, and obtain the beam envelope equation. According to the Poincare–Lyapunov theorem, we analyze the stability of beam envelope equation and find the beam halo. The soliton control method for controlling the beam halo-chaos is put forward based on mechanism of halo formation and strategy of controlling beam halo-chaos, and we also prove the validity of the control method, and furthermore, the feasible experimental project is given. We perform multiparticle simulation to control the halo by using the soliton controller. It is shown that our control method is effective. We also find the radial ion density changes when the ion beam is in the channel, not only the halo-chaos and its regeneration can be eliminated by using the nonlinear control method, but also the density uniformity can be found at beams centre as long as an appropriate control method is chosen.

Sensitivity of Exponents of Three-Power Laws to Hybrid Ratio in Weighted HUHPM

The sensitivity of exponents of three-power laws for node degree, node strength and edged weight to hybrid ratio are studied analytically and numerically in the weighted harmonious unifying hybrid preferential model (HUHPM), which is extended from un-weighted hybrid preferential attachment model we proposed previously [Chin. Phys. Lett. 22 (2005) 719]. Our weighted HUHPMs plus the Barrat–Barthelemy–Vespignani model and the traffic-driven evolution model, respectively, are taken as two typical examples for demonstration and application of the HUHPM.

Advances in theoretical models of network science

In this review article, we will summarize the main advances in network science investigated by the CIAE Group of Complex Network in this field. Several theoretical models of network science were proposed and their topological and dynamical properties are reviewed and compared with the other models. Our models mainly include a harmonious unifying hybrid preferential model, a large unifying hybrid network model, a quantum interference network, a hexagonal nanowire network, and a small-world network with the same degree. The models above reveal some new phenomena and findings, which are useful for deeply understanding and investigating complex networks and their applications.

Synchronization and Bifurcation of General Complex Dynamical Networks

In the present paper, synchronization and bifurcation of general complex dynamical networks are investigated. We mainly focus on networks with a somewhat general coupling matrix, i.e., the sum of each row equals a nonzero constant u. We derive a result that the networks can reach a new synchronous state, which is not the asymptotic limit set determined by the node equation. At the synchronous state, the networks appear bifurcation if we regard the constant u as a bifurcation parameter. Numerical examples are given to illustrate our derived conclusions.

Transition Features from Simplicity-Universality to Complexity-Diversification Under UHNTF ∗

A large unified hybrid network model with a variable speed growth (LUHNM-VSG) is proposed as third model of the unified hybrid network theoretical framework (UHNTF). A hybrid growth ratio vg of deterministic linking number to random linking number and variable speed growth indexare introduced in it. The main effects of vg and � on topological transition features of the LUHNM-VSG are revealed. For comparison with the other models, we construct a type of the network complexity pyramid with seven levels, in which from the bottom level-1 to the top level-7 of the pyramid simplicity-universality is increasing but complexity-diversity is decreasing. The transition relations between them depend on matching of four hybrid ratios (dr, fd, gr, vg). Thus the most of network models can be investigated in the unification way via four hybrid ratios (dr, fd, gr, vg). The LUHNM-VSG as the level-1 of the pyramid is much better and closer to description of real-world networks as well as has potential application.

Synchronization and Bifurcation Analysis in Coupled Networks of Discrete-Time Systems

Synchronization and bifurcation analysis in coupled networks of discrete-time systems are investigated in the present paper. We mainly focus on some special coupling matrix, i.e., the sum of each row equals a nonzero constant u and the network connection is directed. A result that the network can reach a new synchronous state, which is not the asymptotic limit set determined by the node state equation, is derived. It is interesting that the network exhibits bifurcation if we regard the constant u as a bifurcation parameter at the synchronous state. Numerical simulations are given to show the eciency of our derived conclusions.

Certain Properties of a Quantum Information Network Driven by External Fields

A quantum information network with the structure of the Gaussian channel is proposed. The network topological property and information characteristic is studied. Under the catastrophic and exponential external field driving, the degree distribution has the spatial and temporal characteristics, and the positive or negative power index appears, which can influence the assortativity coefficient. This is possibly helpful to open a way to using the different type of driving to introduce the expected properties for the network.

Nonlinear Control of Beam Halo-Chaos in Accelerator-Driven Clean Nuclear Power System*

Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry, medicine, and national defense. Some general engineering methods for chaos control have been developed in recent years, but they generally are unsuccessful for beam halo-chaos suppression due to many technical constraints. Beam halo-chaos is essentially a spatiotemporal chaotic motion within a high power proton accelerator. In this paper, some efficient nonlinear control methods, including wavelet function feedback control as a special nonlinear control method, are proposed for controlling beam halo-chaos under five kinds of the initial proton beam distributions (i.e., Kapchinsky–Vladimirsky, full Gauss, 3-sigma Gauss, water-bag, and parabola distributions) respectively. Particles-in-cell simulations show that after control of beam halo-chaos, the beam halo strength factor is reduced to zero, and other statistical physical quantities of beam halo-chaos are doubly reduced. The methods we developed is very effective for suppression of proton beam halo-chaos in a periodic focusing channel of accelerator. Some potential application of the beam halo-chaos control in experiments is finally pointed out.

Controlling Hopf bifurcations: continuous-time systems

Bifurcation control has attracted increasing attention in recent years. A simple and unified state-feedback method is developed in this paper for Hopf bifurcation control for continuous-time systems. The control task can be either shifting an existing Hopf bifurcation or creating a new Hopf bifurcation. Some computer simulations are included to illustrate the method and verify the theoretical results.