Along with the further development of science and technology, computer hardware and the Intemet are in a rapid development, and information technology has been widely used in all fields so that complex problems are si...Along with the further development of science and technology, computer hardware and the Intemet are in a rapid development, and information technology has been widely used in all fields so that complex problems are simply solved. Because of the needs for the development, software starts to mutually integrate with complex power network, making the scale of software increase greatly. Such a growing trend of software promotes soft-ware development to go beyond a general understanding and control and thus a complex system is formed. It is necessary to strengthen the research of complex network theory, and this is a new way to help people study the complexity of software systems. In this paper, the development course of complex dynamic network is introduced simply and the use of complex power network in the software engineering is summarized. Hopefully, this paper can help the crossover study of complex power network and software engineering in the future.展开更多
In this paper,a series of major policy decisions used to improve the power grid reliability,reduce the risk and losses of major power outages,and realize the modernization of 21st century power grid are discussed. The...In this paper,a series of major policy decisions used to improve the power grid reliability,reduce the risk and losses of major power outages,and realize the modernization of 21st century power grid are discussed. These decisions were adopted by American government and would also be helpful for the strategic development of Chinese power grid. It is proposed that China should take precaution,carry out security research on the overall dynamic behaviour characteristics of the UHV grid using the complexity theory,and finally provide safeguard for the Chinese UHV grid. It is also pointed out that,due to the lack of matured approaches to controll a cascading failure,the primary duty of a system operator is to work as a "watchdog" for the grid operation security,eliminate the cumulative effect and reduce the risk and losses of major cascading outages with the help of EMS and WAMS.展开更多
Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power ...Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power quality classification techniques focused on single power quality events and did not include an optimal feature selection process. This paper presents a classification system that employs Wavelet Transform and the RMS profile to extract the main features of the measured waveforms containing either single or complex disturbances. A data mining process is designed to select the optimal set of features that better describes each disturbance present in the waveform. Support Vector Machine binary classifiers organized in a “One Vs Rest” architecture are individually optimized to classify single and complex disturbances. The parameters that rule the performance of each binary classifier are also individually adjusted using a grid search algorithm that helps them achieve optimal performance. This specialized process significantly improves the total classification accuracy. Several single and complex disturbances were simulated in order to train and test the algorithm. The results show that the classifier is capable of identifying >99% of single disturbances and >97% of complex disturbances.展开更多
A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the ...A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research. Furthermore, it is verified to have higher goodness-of-fit than graphical methods by comparing the KS （Kolmogorov-Smirnov） test statistics for 10 CNN （Connecting Nearest-Neighbor） networks.展开更多
It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One exampl...It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One example is the scale-freeness which is described by the degree distribution in the power law shape. In this paper, within an analytical approach, we investigate the analytical conditions under which the distribution is reduced to the power law. We show that power law distributions are obtained without introducing conditions specific to each system or variable. Conversely, if we demand no special condition to a distribution, it is imposed to follow the power law. This result explains the universality and the ubiquitous presence of the power law distributions in complex networks.展开更多
To analyze and control complex networks effectively, this paper puts forward a new kind of scheme, which takes control separately in each area and can achieve the network’s coordinated optimality. The proposed algori...To analyze and control complex networks effectively, this paper puts forward a new kind of scheme, which takes control separately in each area and can achieve the network’s coordinated optimality. The proposed algorithm is made up of two parts: the first part decomposes the network into several independent areas based on community structure and decouples the information flow and control power among areas; the second part selects the center nodes from each area with the help of the control centrality index. As long as the status of center nodes is kept on a satisfactory level in each area, the whole system is under effective control. Finally, the algorithm is applied to power grids, and the simulations prove its effectiveness.展开更多
Collision detection mechanisms in Wireless Sensor Networks (WSNs) have largely been revolving around direct demodulation and decoding of received packets and deciding on a collision based on some form of a frame error...Collision detection mechanisms in Wireless Sensor Networks (WSNs) have largely been revolving around direct demodulation and decoding of received packets and deciding on a collision based on some form of a frame error detection mechanism, such as a CRC check. The obvious drawback of full detection of a received packet is the need to expend a significant amount of energy and processing complexity in order to fully decode a packet, only to discover the packet is illegible due to a collision. In this paper, we propose a suite of novel, yet simple and power-efficient algorithms to detect a collision without the need for full-decoding of the received packet. Our novel algorithms aim at detecting collision through fast examination of the signal statistics of a short snippet of the received packet via a relatively small number of computations over a small number of received IQ samples. Hence, the proposed algorithms operate directly at the output of the receiver's analog-to-digital converter and eliminate the need to pass the signal through the entire. In addition, we present a complexity and power-saving comparison between our novel algorithms and conventional full-decoding (for select coding schemes) to demonstrate the significant power and complexity saving advantage of our algorithms.展开更多
Wireless relay and network coding are two critical techniques to increase the reliability and throughput of wireless cooperative communication systems. In this paper, a complex field network coding （CFNC） scheme wit...Wireless relay and network coding are two critical techniques to increase the reliability and throughput of wireless cooperative communication systems. In this paper, a complex field network coding （CFNC） scheme with the K-th best relay selection （KBS） is proposed and investigated, wherein the K-th best relay is selected to forward the multiplexed signal to the destination. First, the upper bound of the symbol error probability （SEP）, the diversity order, and the coding gain are derived for the CFNC scheme with KBS. Then, the coding gain is utilized as the optimized cri- terion to determine the optimal power allocation. It is validated through analysis and simulation that the CFNC scheme with KBS can achieve full diversity only when K=I, while the diversity order decreases with increasing parameter K, and the optimal power allocation can significantly improve the performance of the CFNC scheme with KBS.展开更多
A novel framework is established for accurate modeling of Powered Parafoil Unmanned Aerial Vehicle(PPUAV). The model is developed in the following three steps: obtaining a linear dynamic model, simplifying the model s...A novel framework is established for accurate modeling of Powered Parafoil Unmanned Aerial Vehicle(PPUAV). The model is developed in the following three steps: obtaining a linear dynamic model, simplifying the model structure, and estimating the model mismatch due to model variance and external disturbance factors. First, a six degree-of-freedom linear model, or the structured model, is obtained through dynamic establishment and linearization. Second, the data correlation analysis is adopted to determine the criterion for proper model complexity and to simplify the structured model. Next, an active model is established, combining the simplified model with the model mismatch estimator. An adapted Kalman filter is utilized for the real-time estimation of states and model mismatch. We finally derive a linear system model while taking into account of model variance and external disturbance. Actual flight tests verify the effectiveness of our active model in different flight scenarios.展开更多
The main harmonic components in nonlinear differential equations can be solved by using the harmonic balance principle. The nonlinear coupling relation among various harmonics can be found by balance theorem of freque...The main harmonic components in nonlinear differential equations can be solved by using the harmonic balance principle. The nonlinear coupling relation among various harmonics can be found by balance theorem of frequency domain. The superhet receiver circuits which are described by nonlinear differential equation of comprising even degree terms include three main harmonic components: the difference frequency and two signal frequencies. Based on the nonlinear coupling relation, taking superhet circuit as an example, this paper demonstrates that the every one of three main harmonics in networks must individually observe conservation of complex power. The power of difference frequency is from variable-frequency device. And total dissipative power of each harmonic is equal to zero. These conclusions can also be verified by the traditional harmonic analysis. The oscillation solutions which consist of the mixture of three main harmonics possess very long oscillation period, the spectral distribution are very tight, similar to evolution from doubling period leading to chaos. It can be illustrated that the chaos is sufficient or infinite extension of the oscillation period. In fact, the oscillation solutions plotted by numerical simulation all are certainly a periodic function of discrete spectrum. When phase portrait plotted hasn’t finished one cycle, it is shown as aperiodic chaos.展开更多
LT codes are practical realization of digital fountain codes, which provides the concept of rateless coding. In this scheme, encoded symbols are generated infinitely from k information symbols. Decoder uses only(1+α)...LT codes are practical realization of digital fountain codes, which provides the concept of rateless coding. In this scheme, encoded symbols are generated infinitely from k information symbols. Decoder uses only(1+α)k number of encoded symbols to recover the original information. The degree distribution function in the LT codes helps to generate a random graph also referred as tanner graph. The artifact of tanner graph is responsible for computational complexity and overhead in the LT codes. Intuitively, a well designed degree distribution can be used for an efficient implementation of LT codes. The degree distribution function is studied as a function of power law, and LT codes are classified into two different categories: SFLT and RLT codes. Also, two different degree distributions are proposed and analyzed for SFLT codes which guarantee optimal performance in terms of computational complexity and overhead.展开更多
The power-density function of the noise spectrum of open and complex systems changes by the power of frequency. We show that the fluctuation origin and the noise-powered description are equivalent to describe the colo...The power-density function of the noise spectrum of open and complex systems changes by the power of frequency. We show that the fluctuation origin and the noise-powered description are equivalent to describe the colored noise power density. Based on this, we introduce a scale-independent invariant for monitoring the dynamics of the complex system. The monitoring of the noise spectrum of the system specifies the forecast of failure, the timing of desired regular corrections and/or the assessed operation life of the system, indicating the possible faults before it happens, predicting deterioration like wear/tear, fatigue in the still properly working system. These considerations are highly applicable to living systems and their preventive care.展开更多
In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol ...In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.展开更多
Complex networks have been widely studied. Recently,many results show that the degree distributions of some large networks follow the form of power-law and these networks possess better robustness against random nodes...Complex networks have been widely studied. Recently,many results show that the degree distributions of some large networks follow the form of power-law and these networks possess better robustness against random nodes failure. As an effective technology on combating the channel fading,wireless cooperative communication is becoming one of the most important methods to improve the wireless communication performances. In this paper,the complex network models based on cooperative communication and non-cooperative communication are established; and the degree distribution properties for them are studied. The simulation results show that the degree distributions of these networks also follow the form of power-law,which means that the addition of cooperative communi-cation links will not change the property of degree distribution and then these networks will possess better robustness against random nodes failure as well.展开更多
In this paper, a new topological approach for studying an integer sequence constructed from Logistic mapping is proposed. By evenly segmenting [0,1]?into N non-overlapping subintervals which is marked as , representin...In this paper, a new topological approach for studying an integer sequence constructed from Logistic mapping is proposed. By evenly segmenting [0,1]?into N non-overlapping subintervals which is marked as , representing the nodes identities, a network is constructed for analysis. Wherein the undirected edges symbolize their relation of adjacency in an integer sequence obtained from the Logistic mapping and the top integral function. By observation, we find that nodes’ degree changes with different values of??instead of the initial value—X0, and the degree distribution presents the characteristics of scale free network, presenting power law distribution. The results presented in this paper provide some insight into degree distribution of the network constructed from integer sequence that may help better understanding of the nature of Logistic mapping.展开更多
This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolut...This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well.展开更多
文摘Along with the further development of science and technology, computer hardware and the Intemet are in a rapid development, and information technology has been widely used in all fields so that complex problems are simply solved. Because of the needs for the development, software starts to mutually integrate with complex power network, making the scale of software increase greatly. Such a growing trend of software promotes soft-ware development to go beyond a general understanding and control and thus a complex system is formed. It is necessary to strengthen the research of complex network theory, and this is a new way to help people study the complexity of software systems. In this paper, the development course of complex dynamic network is introduced simply and the use of complex power network in the software engineering is summarized. Hopefully, this paper can help the crossover study of complex power network and software engineering in the future.
文摘In this paper,a series of major policy decisions used to improve the power grid reliability,reduce the risk and losses of major power outages,and realize the modernization of 21st century power grid are discussed. These decisions were adopted by American government and would also be helpful for the strategic development of Chinese power grid. It is proposed that China should take precaution,carry out security research on the overall dynamic behaviour characteristics of the UHV grid using the complexity theory,and finally provide safeguard for the Chinese UHV grid. It is also pointed out that,due to the lack of matured approaches to controll a cascading failure,the primary duty of a system operator is to work as a "watchdog" for the grid operation security,eliminate the cumulative effect and reduce the risk and losses of major cascading outages with the help of EMS and WAMS.
文摘Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power quality classification techniques focused on single power quality events and did not include an optimal feature selection process. This paper presents a classification system that employs Wavelet Transform and the RMS profile to extract the main features of the measured waveforms containing either single or complex disturbances. A data mining process is designed to select the optimal set of features that better describes each disturbance present in the waveform. Support Vector Machine binary classifiers organized in a “One Vs Rest” architecture are individually optimized to classify single and complex disturbances. The parameters that rule the performance of each binary classifier are also individually adjusted using a grid search algorithm that helps them achieve optimal performance. This specialized process significantly improves the total classification accuracy. Several single and complex disturbances were simulated in order to train and test the algorithm. The results show that the classifier is capable of identifying >99% of single disturbances and >97% of complex disturbances.
基金Project supported by the National Natural Science Foundation of China (Nos.70431002, 70401019)
文摘A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research. Furthermore, it is verified to have higher goodness-of-fit than graphical methods by comparing the KS （Kolmogorov-Smirnov） test statistics for 10 CNN （Connecting Nearest-Neighbor） networks.
文摘It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One example is the scale-freeness which is described by the degree distribution in the power law shape. In this paper, within an analytical approach, we investigate the analytical conditions under which the distribution is reduced to the power law. We show that power law distributions are obtained without introducing conditions specific to each system or variable. Conversely, if we demand no special condition to a distribution, it is imposed to follow the power law. This result explains the universality and the ubiquitous presence of the power law distributions in complex networks.
基金the National Science Foundation of China (No.50525721, 50595411)the National Basic Research Program of China(No.G2004CB217902)
文摘To analyze and control complex networks effectively, this paper puts forward a new kind of scheme, which takes control separately in each area and can achieve the network’s coordinated optimality. The proposed algorithm is made up of two parts: the first part decomposes the network into several independent areas based on community structure and decouples the information flow and control power among areas; the second part selects the center nodes from each area with the help of the control centrality index. As long as the status of center nodes is kept on a satisfactory level in each area, the whole system is under effective control. Finally, the algorithm is applied to power grids, and the simulations prove its effectiveness.
文摘Collision detection mechanisms in Wireless Sensor Networks (WSNs) have largely been revolving around direct demodulation and decoding of received packets and deciding on a collision based on some form of a frame error detection mechanism, such as a CRC check. The obvious drawback of full detection of a received packet is the need to expend a significant amount of energy and processing complexity in order to fully decode a packet, only to discover the packet is illegible due to a collision. In this paper, we propose a suite of novel, yet simple and power-efficient algorithms to detect a collision without the need for full-decoding of the received packet. Our novel algorithms aim at detecting collision through fast examination of the signal statistics of a short snippet of the received packet via a relatively small number of computations over a small number of received IQ samples. Hence, the proposed algorithms operate directly at the output of the receiver's analog-to-digital converter and eliminate the need to pass the signal through the entire. In addition, we present a complexity and power-saving comparison between our novel algorithms and conventional full-decoding (for select coding schemes) to demonstrate the significant power and complexity saving advantage of our algorithms.
基金supported by the Major State Basic Research Development Program of China(973 Program No.2012CB316100)the National Natural Science Foundation of China(Nos.61032002/61271246)the 111 Project(No.111-2-14)
文摘Wireless relay and network coding are two critical techniques to increase the reliability and throughput of wireless cooperative communication systems. In this paper, a complex field network coding （CFNC） scheme with the K-th best relay selection （KBS） is proposed and investigated, wherein the K-th best relay is selected to forward the multiplexed signal to the destination. First, the upper bound of the symbol error probability （SEP）, the diversity order, and the coding gain are derived for the CFNC scheme with KBS. Then, the coding gain is utilized as the optimized cri- terion to determine the optimal power allocation. It is validated through analysis and simulation that the CFNC scheme with KBS can achieve full diversity only when K=I, while the diversity order decreases with increasing parameter K, and the optimal power allocation can significantly improve the performance of the CFNC scheme with KBS.
基金co-supported by the National Nature Sciences Foundation of China (Nos. 61503369 and 61528303)the State Key Laboratory of Roboticsthe Chinese National Key Technology R&D Program (No. Y4A12081010)
文摘A novel framework is established for accurate modeling of Powered Parafoil Unmanned Aerial Vehicle(PPUAV). The model is developed in the following three steps: obtaining a linear dynamic model, simplifying the model structure, and estimating the model mismatch due to model variance and external disturbance factors. First, a six degree-of-freedom linear model, or the structured model, is obtained through dynamic establishment and linearization. Second, the data correlation analysis is adopted to determine the criterion for proper model complexity and to simplify the structured model. Next, an active model is established, combining the simplified model with the model mismatch estimator. An adapted Kalman filter is utilized for the real-time estimation of states and model mismatch. We finally derive a linear system model while taking into account of model variance and external disturbance. Actual flight tests verify the effectiveness of our active model in different flight scenarios.
文摘The main harmonic components in nonlinear differential equations can be solved by using the harmonic balance principle. The nonlinear coupling relation among various harmonics can be found by balance theorem of frequency domain. The superhet receiver circuits which are described by nonlinear differential equation of comprising even degree terms include three main harmonic components: the difference frequency and two signal frequencies. Based on the nonlinear coupling relation, taking superhet circuit as an example, this paper demonstrates that the every one of three main harmonics in networks must individually observe conservation of complex power. The power of difference frequency is from variable-frequency device. And total dissipative power of each harmonic is equal to zero. These conclusions can also be verified by the traditional harmonic analysis. The oscillation solutions which consist of the mixture of three main harmonics possess very long oscillation period, the spectral distribution are very tight, similar to evolution from doubling period leading to chaos. It can be illustrated that the chaos is sufficient or infinite extension of the oscillation period. In fact, the oscillation solutions plotted by numerical simulation all are certainly a periodic function of discrete spectrum. When phase portrait plotted hasn’t finished one cycle, it is shown as aperiodic chaos.
基金supported by Research Fund Chosun Univerity,2011
文摘LT codes are practical realization of digital fountain codes, which provides the concept of rateless coding. In this scheme, encoded symbols are generated infinitely from k information symbols. Decoder uses only(1+α)k number of encoded symbols to recover the original information. The degree distribution function in the LT codes helps to generate a random graph also referred as tanner graph. The artifact of tanner graph is responsible for computational complexity and overhead in the LT codes. Intuitively, a well designed degree distribution can be used for an efficient implementation of LT codes. The degree distribution function is studied as a function of power law, and LT codes are classified into two different categories: SFLT and RLT codes. Also, two different degree distributions are proposed and analyzed for SFLT codes which guarantee optimal performance in terms of computational complexity and overhead.
文摘The power-density function of the noise spectrum of open and complex systems changes by the power of frequency. We show that the fluctuation origin and the noise-powered description are equivalent to describe the colored noise power density. Based on this, we introduce a scale-independent invariant for monitoring the dynamics of the complex system. The monitoring of the noise spectrum of the system specifies the forecast of failure, the timing of desired regular corrections and/or the assessed operation life of the system, indicating the possible faults before it happens, predicting deterioration like wear/tear, fatigue in the still properly working system. These considerations are highly applicable to living systems and their preventive care.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70871082)the Shanghai Leading Academic Discipline Project (Grant No. S30504)
文摘In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.
基金Supported by Shanghai Leading Academic Discipline Project under Grant T0102,Fund of Innovation for Graduate Student of Shanghai University (No.shucx080151)Youth Innovation Foundation of SIMIT,CAS (No.2008QNCX03)
文摘Complex networks have been widely studied. Recently,many results show that the degree distributions of some large networks follow the form of power-law and these networks possess better robustness against random nodes failure. As an effective technology on combating the channel fading,wireless cooperative communication is becoming one of the most important methods to improve the wireless communication performances. In this paper,the complex network models based on cooperative communication and non-cooperative communication are established; and the degree distribution properties for them are studied. The simulation results show that the degree distributions of these networks also follow the form of power-law,which means that the addition of cooperative communi-cation links will not change the property of degree distribution and then these networks will possess better robustness against random nodes failure as well.
文摘In this paper, a new topological approach for studying an integer sequence constructed from Logistic mapping is proposed. By evenly segmenting [0,1]?into N non-overlapping subintervals which is marked as , representing the nodes identities, a network is constructed for analysis. Wherein the undirected edges symbolize their relation of adjacency in an integer sequence obtained from the Logistic mapping and the top integral function. By observation, we find that nodes’ degree changes with different values of??instead of the initial value—X0, and the degree distribution presents the characteristics of scale free network, presenting power law distribution. The results presented in this paper provide some insight into degree distribution of the network constructed from integer sequence that may help better understanding of the nature of Logistic mapping.
基金supported by the National Natural Science Foundation of China(Grant No.70871082)the Shanghai Leading Academic Discipline Project,China(Grant No.S30504)
文摘This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well.
