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 on 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.
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 oscillations,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.
一个网络是如果它由 N 节点组成，混合了网络被说出，一些节点的动力学是周期的，当其它是混乱的时。有联合的 all-to-all 的混合网络和它在修剪的非线性差距条件以后的相应网络被调查。几个同步状态在两个系统被表明，并且一阶的阶段转变被建议。动力学的混合暗示为整个网络的任何种同步动力学，和混合网络可以被修剪的非线性差距条件控制。
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 hidden.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 higherorder 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 searching 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) = A cos 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 T0 I(t) ei ω tdt. 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.
