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论文范文
1. Introduction Complex systems are common in engineering, examples being communication networks, computer networks, and electronic devices, as well as mechanical systems such as manufacturing plants, aircrafts, and automobiles. Determining the dynamic behavior of these mechanical systems requires the use of advanced analytical techniques. As the number of elements increases, simple systems evolve into ones that are more complex. Concepts such as correlation dimension, Lyapunov exponents, fractal properties, and complex network analysis are some of ideas that are used to determine dynamic properties. The problem is to identify the source of synchronization from field data. In addition to other behavioral characteristics, complex systems can present synchronization. In most cases, the system deploys two behaviors: one that is easily identified at a foreground level and another that remains at background level [1]. The foreground behavior is seen at frequency responses with high amplitudes and narrow bands, whereas the background behavior presents a wide band response and low amplitudes. The study of synchronization has been an exciting and interesting problem since Huygens first wrote about his experiments in 1665 [2]. Peña Ramirez et al. [3] analyzed Huygens’ experiment, modeling the system as a lumped mass model, and found that synchronization depends on the relationship between the masses, the stiffness of the connecting beam, and the amount of damping in the system. Keeffe et al. [4] presented a model for the analysis of pulse coupled oscillators. As they described it: in some systems synchronization starts at a certain location and expands forming clusters. They suggested that clusters formed, evolved, and collapsed. For this purpose, they developed a model that provides an idea of the physical phenomena and how clusters evolved into synchronization. They described different systems that behave as pulse coupled oscillators. They presented two types of oscillators, systems with local coupling and systems with global coupling. There is still a question how transient dynamics leads to synchronization [4]. Ulrichs et al. [5] presented the analysis of metronomes as nonlinear periodic oscillators. The metronomes behave asymptotically and they show higher dimensional attractors. Metronomes have the same behavior as Huygens clocks, and their synchronization can be modeled using Kuramoto’s parameter. They found small traveling waves through the system support that lock the phase difference among all metronomes and they model the connections in terms of a Van der Pol oscillator. Aragonès and Guasch [6] presented a theoretical analysis of path propagation in a set of systems with similar structures. Woodhouse [7] and Langley et al. [8, 9] introduced statistical energy analysis. They modeled the system as a set of springs and represented it as a block diagram. The diagram represented subsystems as blocks and power flows as connections among subsystems. For the net analysis, they assigned weight factors relating a coupling loss factor to a total loss factor. Moreover, they dealt with the net analysis including a probabilistic density function and computed the weight factors as a statistical ratio. They defined the length of a particular link as a random variable, and they defined this function as a mean function plus a function of the standard deviation. A similar approach was presented by Llerena-Aguilar et al. [10]. They reported a hybrid method for the analysis of wave propagation and synchronization of a Wireless Acoustic Sensor (microphones) Networks. The problem they solved is the inverse of what we are trying to understand. In fact, they studied the desynchronization. The phenomenon is caused by two factors, namely, the clock phase offset of each sensor and the propagation delay due to the distance between them. These factors are critical in the selection of the processing algorithm. The classical solution was the implementation of clock synchronization protocols. The phenomenon is simulated assuming that the source signals are received by an array of sensors. Then, the signals are combined adding a Gaussian noise and convoluting the signal with an impulse function for each sensor. 
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