All dynamic complex networks have two important aspects, pattern dynamics and network topology. Discovering different types of pattern dynamics and exploring how these dynamics depend or/network topologies are tasks of both great theoretical importance and broad practical significance. In this paper we study the oscillatory behaviors of excitable complex networks （ECNs） and find some interesting dynamic behaviors of ECNs in oscillatory probability, the multiplicity of oscillatory attractors, period distribution, and different types of oscillatory patterns （e.g., periodic, quasiperiodic, and chaotic）. In these aspects, we further explore strikingly sharp differences among network dynamics induced by different topologies （random or scale-free topologies） and different interaction structures （symmetric or asymmetric couplings）. The mechanisms behind these differences are explained physically.
In this work, we study the collective dynamics of phase oscillators in a mobile ad hoc network whose topology changes dynamically. As the network size or the communication radius of individual oscillators increases, the topology of the ad hoc network first undergoes percolation, forming a giant cluster, and then gradually achieves global connectivity. It is shown that oscillator mobility generally enhances the coherence in such networks. Interestingly, we find a new type of phase synchronization/clustering, in which the phases of the oscillators are distributed in a certain narrow range, while the instantaneous frequencies change signs frequently, leading to shuttle-run-like motion of the oscillators in phase space. We conduct a theoretical analysis to explain the mechanism of this synchronization and obtain the critical transition point.
This review describes the investigations of oscillatory complex networks consisting of excitable nodes, focusing on the target wave patterns or say the target wave attractors. A method of dominant phase advanced driving （DPAD） is introduced to reveal the dynamic structures in the networks supporting osciUations, such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks. The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns. Therefore, the center （say node A） and its driver （say node B） of a target wave can be used as a label, （A, B）, of the given target pattern. The label can give a clue to conveniently retrieve, suppress, and control the target waves. Statistical investigations, both theoretically from the label analysis and numerically from direct simulations of network dynamics, show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large, and all these attractors can be labeled and easily controlled based on the information given by the labels. The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.
A network is named as mixed network if it is composed of N nodes, the dynamics of some nodes are periodic, while the others are chaotic. The mixed network with all-to-all coupling and its correspond- ing networks after the nonlinearity gap-condition pruning are investigated. Several synchronization states are demonstrated in both systems, and a first-order phase transition is proposed. The mixture of dynamics implies any kind of synchronous dynamics for the whole network, and the inixed networks may be controlled by the nonlinearity gap-condition pruning.
The problem of network reconstruction, particularly exploring unknown network structures by analyzing measurable output data from networks, has attracted significant interest in many interdisciplinary fields in recent times. In practice, networks may be very large, and data can often be measured for only some of the nodes in a network while data for other variables are bidden. It is thus crucial to be able to infer networks from partial data. In this article, we study the problem of noise-driven nonlinear networks with some hidden nodes. Various difficulties appear jointly： nonlinearity of network dynamics, the impact of strong noise, the complexity of interaction structures between network nodes, and missing data from certain hidden nodes. We propose using high-order correlation to treat nonlinearity and structural complexity, two-time correlation to decorrelate noise, and higher- order derivatives to overcome the difficulties of hidden nodes. A closed form of network reconstruction is derived, and numerical simulations confirm the theoretical predictions.
Yang ChenChao Yang ZhangTian Yu ChenShi Hong WangGang Hu
Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The search- ing for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation （or Weyl equation） and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different, rendering distinct level spacing statistics.
Signal detection is both a fundamental topic of data science and a great challenge for practical engineering. One of the canonical tasks widely investigated is detecting a sinusoidal signal of known frequency ω with time duration T：I（t）=Acos ω t＋Γ（t）, embedded within a stationary noisy data. The most direct, and also believed to be the most efficient, method is to compute the Fourier spectral power at ω：B=｜2/T∫0^T I（t）e^iωtdt｜. Whether one can out-perform the linear Fourier approach by any other nonlinear processing has attracted great interests but so far without a consensus. Neither a rigorous analytic theory has been offered. We revisit the problem of weak signal, strong noise, and finite data length T=O（1）, and propose a signal detection method based on resonant filtering. While we show that the linear approach of resonant filters yield a same signal detection efficiency in the limit of T→∞, for finite time length T=O（1）, our method can improve the signal detection due to the highly nonlinear interactions between various characteristics of a resonant filter in finite time with respect to transient evolution. At the optimal match between the input I（t）, the control parameters, and the initial preparation of the filter state, its performance exceeds the above threshold B considerably. Our results are based on a rigorous analysis of Gaussian processes and the conclusions are supported by numerical computations.
