Evolutionary studies have been of prime importance to life scientists since ancient times. The advancements in technology has made it possible to make available the massive amounts of genomic data. The abundance of ge...Evolutionary studies have been of prime importance to life scientists since ancient times. The advancements in technology has made it possible to make available the massive amounts of genomic data. The abundance of genomic data poses new challenges for biologists, computer scientists and mathematicians to develop approaches for discovery of new relationships in data and evolutionary networks. In this work, nucleotide sequences are converted into binary sequences to explore the network among different species. A new approach based on binary sequences has been proposed to reconstruct the accurate phylogenetic network. The algorithm developed is validated by comparing the results with those obtained by already existing method of network construction. A program is also coded in C language on the Intel Core i3 Dell inspiron machine to obtain the evolutionary network. The new approach developed also provides the fast solutions as there is no need of aligning the sequences.展开更多
Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games(NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic ex...Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games(NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic expression is formulated for the networked evolutionary games with finite memories, based on which the behavior of the corresponding evolutionary game is analyzed. Secondly, under a proper assumption, the existence of Nash equilibrium of the given networked evolutionary games is proved and a free-type strategy sequence is designed for the convergence to the Nash equilibrium. Finally, an illustrative example is worked out to support the obtained new results.展开更多
We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner's dilemma game (PDG) in one l...We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner's dilemma game (PDG) in one layer and snowdrift game (SDG) in the other. We explore the dependences of the fraction of the strategy cooperation in different layers on the game parameter and initial conditions. The results on two-layer square lattices show that, when cooperation is the dominant strategy, initial conditions strongly influence cooperation in the PDG layer while have no impact in the SDG layer. Moreover, in contrast to the result for PDG in single-layer square lattices, the parameter regime where cooperation could be maintained expands significantly in the PDG layer. We also investigate the effects of mutation and network topology. We find that different mutation rates do not change the cooperation behaviors. Moreover, similar behaviors on cooperation could be found in two-layer random networks.展开更多
In Internet of Things(IoT), the devices or terminals are connected with each other, which can be very diverse over the wireless networks. Unfortunately, the current devices are not designed to communicate with the col...In Internet of Things(IoT), the devices or terminals are connected with each other, which can be very diverse over the wireless networks. Unfortunately, the current devices are not designed to communicate with the collocated devices which employ different communication technologies. Consequently, the communication between these devices will be realized only by using the gateway nodes. This will cause the inefficient use of wireless resources. Therefore, in this paper, a smart service system(SSS) architecture is proposed, which consists of smart service terminal(SST), and smart service network(SSN), to realize the Io T in a general environment with diverse communication networks, devices, and services. The proposed architecture has the following advantages: i) the devices in this architecture cover multiple types of terminals and sensor-actuator devices; ii) the communications network therein is a converged network, and will coordinate multiple kinds of existing and emerging networks. This converged network offers ubiquitous access for various sensors and terminals; iii) the architecture has services and applications covering all smart service areas. It also provides theadaptability to new services and applications. A SSS architecture-based smart campus system was developed and deployed. Evaluation experiments of the proposed smart campus system demonstrate the SSS's advantages over the existing counterparts, and verify the effectiveness of the proposed architecture.展开更多
Generative adversarial networks(GANs)have considerable potential to alleviate challenges linked to data scarcity.Recent research has demonstrated the good performance of this method for data augmentation because GANs ...Generative adversarial networks(GANs)have considerable potential to alleviate challenges linked to data scarcity.Recent research has demonstrated the good performance of this method for data augmentation because GANs synthesize semantically meaningful data from standard signal distribution.The goal of this study was to solve the overfitting problem that is caused by the training process of convolution networks with a small dataset.In this context,we propose a data augmentation method based on an evolutionary generative adversarial network for cardiac magnetic resonance images to extend the training data.In our structure of the evolutionary GAN,the most optimal generator is chosen that considers the quality and diversity of generated images simultaneously from many generator mutations.Also,to expand the distribution of the whole training set,we combine the linear interpolation of eigenvectors to synthesize new training samples and synthesize related linear interpolation labels.This approach makes the discrete sample space become continuous and improves the smoothness between domains.The visual quality of the augmented cardiac magnetic resonance images is improved by our proposed method as shown by the data-augmented experiments.In addition,the effectiveness of our proposed method is verified by the classification experiments.The influence of the proportion of synthesized samples on the classification results of cardiac magnetic resonance images is also explored.展开更多
This study mainly focused on the dynamic self-similar k_(c)-center network as a result of information distribution through social networks.Individual attraction with various preferences was characterized in the model ...This study mainly focused on the dynamic self-similar k_(c)-center network as a result of information distribution through social networks.Individual attraction with various preferences was characterized in the model as a result of reciprocal attraction among individuals and human multi-attribute.Additionally,the model incorporated the community network structure and network evolution mechanism,and a dynamic self-similar k_(c)-center network generation model was presented.Compared with the classical scale-free network generation algorithm,the generated network embodied not only the characteristics of the small-world and scale-free,but also the characteristics of dynamic self-similar k_(c)-center network.The experimental results were verified by comparing the real data with the experimental data.The results showed that there are dynamic self-similar k_(c)-center networks and their internal network relationship dynamics in the micro scale,meso scale and global perspective based on information dissemination.展开更多
This paper investigates the networked evolutionary games(NEGs)with profile-dependent delays,including modeling and stability analysis.Profile-dependent delay,which varies with the game profiles,slows the information t...This paper investigates the networked evolutionary games(NEGs)with profile-dependent delays,including modeling and stability analysis.Profile-dependent delay,which varies with the game profiles,slows the information transmission between participants.Firstly,the dynamics model is proposed for the profile-dependent delayed NEG,then the algebraic formulation is established using the algebraic state space approach.Secondly,the dynamic behavior of the game is discussed,involving general stability and evolutionarily stable profile analysis.Necessary and sufficient criteria are derived using the matrices,which can be easily verified by mathematical software.Finally,a numerical example is carried out to demonstrate the validity of the theoretical results.展开更多
In this paper a comprehensive introduction for modeling and control of networked evolutionary games (NEGs) via semi-tensor product (STP) approach is presented. First, we review the mathematical model of an NEG, wh...In this paper a comprehensive introduction for modeling and control of networked evolutionary games (NEGs) via semi-tensor product (STP) approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients: network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i) undirected graph for symmetric games; ii) directed graph for asymmetric games, and iii) d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games (FEGs) are discussed, which are i) two strategies and symmetric (S-2); ii) two strategies and asymmetric (A-2); and iii) three strategies and symmetric (S-3). Three strategy updating rules (SUR) are introduced, which are i) Unconditional Imitation (UI); ii) Fermi Rule(FR); iii) Myopic Best Response Adjustment Rule (MBRA). First, we review the fundamental evolutionary equation (FEE) and use it to construct network profile dynamics (NPD)of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation (FEE) of each player is discussed. Using FEEs, the network strategy profile dynamics (NSPD) is built by providing efficient algorithms. Finally, we consider three more complicated NEGs: i) NEG with different length historical information, ii) NEG with multi-species, and iii) NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.展开更多
This paper considers the modeling and convergence of hyper-networked evolutionary games (HNEGs). In an HNEG the network graph is a hypergraph, which allows the fundamental network game to be a multi-player one. Usin...This paper considers the modeling and convergence of hyper-networked evolutionary games (HNEGs). In an HNEG the network graph is a hypergraph, which allows the fundamental network game to be a multi-player one. Using semi-tensor product of matrices and the fundamental evolutionary equation, the dynamics of an HNEG is obtained and we extend the results about the networked evolutionary games to show whether an HNEG is potential and how to calculate the potential. Then we propose a new strategy updating rule, called the cascading myopic best response adjustment rule (MBRAR), and prove that under the cascading MBRAR the strategies of an HNEG will converge to a pure Nash equilibrium. An example is presented and discussed in detail to demonstrate the theoretical and numerical results.展开更多
In the present study,a novel approach based on an evolutionary wavelet neural network(EWNN)is proposed to estimate the slag quality in an electric arc furnace(EAF)employing power quality indices.In the EWNN,an evoluti...In the present study,a novel approach based on an evolutionary wavelet neural network(EWNN)is proposed to estimate the slag quality in an electric arc furnace(EAF)employing power quality indices.In the EWNN,an evolutionary method is applied to train the parameters for a combination of neural networks and wavelets.I For this purpose,all of the electrical parameters for six melting processes are measured with a power quality analyzer,attached to the secondary component of an EAF transformer at a Saba steel complex,to estimate the foaming slag quality.Experimental results on various combinations of measured electrical parameters,applying the designed EWNN estimator,demonstrate that utilizing five leading indicators leads to the highest precision.The obtained 99%accuracy for estimating the foaming slag quality by EWNN compared to the other methods illustrates the proposed method's efficiency.展开更多
Evolutionary neural network(ENN)shows high performance in function optimization and in finding approximately global optima from searching large and complex spaces.It is one of the most efficient and adaptive optimizat...Evolutionary neural network(ENN)shows high performance in function optimization and in finding approximately global optima from searching large and complex spaces.It is one of the most efficient and adaptive optimization techniques used widely to provide candidate solutions that lead to the fitness of the problem.ENN has the extraordinary ability to search the global and learning the approximate optimal solution regardless of the gradient information of the error functions.However,ENN requires high computation and processing which requires parallel processing platforms such as field programmable gate arrays(FPGAs)and graphic processing units(GPUs)to achieve a good performance.This work involves different new implementations of ENN by exploring and adopting different techniques and opportunities for parallel processing.Different versions of ENN algorithm have also been implemented and parallelized on FPGAs platform for low latency by exploiting the parallelism and pipelining approaches.Real data form mass spectrometry data(MSD)application was tested to examine and verify our implementations.This is a very important and extensive computation application which needs to search and find the optimal features(peaks)in MSD in order to distinguish cancer patients from control patients.ENN algorithm is also implemented and parallelized on single core and GPU platforms for comparison purposes.The computation time of our optimized algorithm on FPGA and GPU has been improved by a factor of 6.75 and 6,respectively.展开更多
Lacking labeled examples of working numerical strategies,adapting an iterative solver to accommodate a numerical issue,e.g.,density discontinuities in the pressure Poisson equation,is non-trivial and usually involves ...Lacking labeled examples of working numerical strategies,adapting an iterative solver to accommodate a numerical issue,e.g.,density discontinuities in the pressure Poisson equation,is non-trivial and usually involves a lot of trial and error.Here,we resort to evolutionary neural network.A evolutionary neural network observes the outcome of an action and adapts its strategy accordingly.The process requires no labeled data but only a measure of a network’s performance at a task.Applying neuro-evolution and adapting the Jacobi iterative method for the pressure Poisson equation with density discontinuities,we show that the adapted Jacobi method is able to accommodate density discontinuities.展开更多
Basic concepts about the finite potential games and the networked evolutionary games(NEGs)are introduced.Some new developments are surveyed,including(i)formulas for verifying whether a finite game is(weighted)potentia...Basic concepts about the finite potential games and the networked evolutionary games(NEGs)are introduced.Some new developments are surveyed,including(i)formulas for verifying whether a finite game is(weighted)potential and for calculating the(weighted)potential function;and(ii)the fundamental network equation and strategy profile dynamics of NEGs.Then some applications are introduced,which include:(i)convergence of NEGs;(ii)congestion control;(iii)distributed coverage of graphs.展开更多
This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established ...This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established for PTDBN with impulsive effect.Then,based on the probabilistic state transition matrix,a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive effect.Finally,the obtained new result is applied to the networked evolutionary game with memories.展开更多
文摘Evolutionary studies have been of prime importance to life scientists since ancient times. The advancements in technology has made it possible to make available the massive amounts of genomic data. The abundance of genomic data poses new challenges for biologists, computer scientists and mathematicians to develop approaches for discovery of new relationships in data and evolutionary networks. In this work, nucleotide sequences are converted into binary sequences to explore the network among different species. A new approach based on binary sequences has been proposed to reconstruct the accurate phylogenetic network. The algorithm developed is validated by comparing the results with those obtained by already existing method of network construction. A program is also coded in C language on the Intel Core i3 Dell inspiron machine to obtain the evolutionary network. The new approach developed also provides the fast solutions as there is no need of aligning the sequences.
基金supported by the National Natural Science Foundation of China(61503225)the Natural Science Foundation of Shandong Province(ZR2015FQ003,ZR201709260273)
文摘Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games(NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic expression is formulated for the networked evolutionary games with finite memories, based on which the behavior of the corresponding evolutionary game is analyzed. Secondly, under a proper assumption, the existence of Nash equilibrium of the given networked evolutionary games is proved and a free-type strategy sequence is designed for the convergence to the Nash equilibrium. Finally, an illustrative example is worked out to support the obtained new results.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11575036,71301012,and 11505016
文摘We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner's dilemma game (PDG) in one layer and snowdrift game (SDG) in the other. We explore the dependences of the fraction of the strategy cooperation in different layers on the game parameter and initial conditions. The results on two-layer square lattices show that, when cooperation is the dominant strategy, initial conditions strongly influence cooperation in the PDG layer while have no impact in the SDG layer. Moreover, in contrast to the result for PDG in single-layer square lattices, the parameter regime where cooperation could be maintained expands significantly in the PDG layer. We also investigate the effects of mutation and network topology. We find that different mutation rates do not change the cooperation behaviors. Moreover, similar behaviors on cooperation could be found in two-layer random networks.
基金supported by the national 973 project of China under Grants 2013CB329104the Natural Science Foundation of China under Grants 61372124, 61427801+1 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No.13KJB520029)the Jiangsu Province colleges and universities graduate students scientific research and innovation program CXZZ13_0477,NUPTSF(Grant No.NY214033)
文摘In Internet of Things(IoT), the devices or terminals are connected with each other, which can be very diverse over the wireless networks. Unfortunately, the current devices are not designed to communicate with the collocated devices which employ different communication technologies. Consequently, the communication between these devices will be realized only by using the gateway nodes. This will cause the inefficient use of wireless resources. Therefore, in this paper, a smart service system(SSS) architecture is proposed, which consists of smart service terminal(SST), and smart service network(SSN), to realize the Io T in a general environment with diverse communication networks, devices, and services. The proposed architecture has the following advantages: i) the devices in this architecture cover multiple types of terminals and sensor-actuator devices; ii) the communications network therein is a converged network, and will coordinate multiple kinds of existing and emerging networks. This converged network offers ubiquitous access for various sensors and terminals; iii) the architecture has services and applications covering all smart service areas. It also provides theadaptability to new services and applications. A SSS architecture-based smart campus system was developed and deployed. Evaluation experiments of the proposed smart campus system demonstrate the SSS's advantages over the existing counterparts, and verify the effectiveness of the proposed architecture.
基金funding in part from the Sichuan Science and Technology Program(http://kjt.sc.gov.cn/)under Grant 2019ZDZX0005the Chinese Scholarship Council(https://www.csc.edu.cn/)under Grant 201908515022.
文摘Generative adversarial networks(GANs)have considerable potential to alleviate challenges linked to data scarcity.Recent research has demonstrated the good performance of this method for data augmentation because GANs synthesize semantically meaningful data from standard signal distribution.The goal of this study was to solve the overfitting problem that is caused by the training process of convolution networks with a small dataset.In this context,we propose a data augmentation method based on an evolutionary generative adversarial network for cardiac magnetic resonance images to extend the training data.In our structure of the evolutionary GAN,the most optimal generator is chosen that considers the quality and diversity of generated images simultaneously from many generator mutations.Also,to expand the distribution of the whole training set,we combine the linear interpolation of eigenvectors to synthesize new training samples and synthesize related linear interpolation labels.This approach makes the discrete sample space become continuous and improves the smoothness between domains.The visual quality of the augmented cardiac magnetic resonance images is improved by our proposed method as shown by the data-augmented experiments.In addition,the effectiveness of our proposed method is verified by the classification experiments.The influence of the proportion of synthesized samples on the classification results of cardiac magnetic resonance images is also explored.
基金the National Natural Science Foundation of China (No.62062010)the Program for the Science and Technology Planning Project of Guangxi (No.AD19245101)the Program for the Longyuan Youth Innovation and Entrepreneurship Talent Team Project of Gansu (No.2021LQTD24)。
文摘This study mainly focused on the dynamic self-similar k_(c)-center network as a result of information distribution through social networks.Individual attraction with various preferences was characterized in the model as a result of reciprocal attraction among individuals and human multi-attribute.Additionally,the model incorporated the community network structure and network evolution mechanism,and a dynamic self-similar k_(c)-center network generation model was presented.Compared with the classical scale-free network generation algorithm,the generated network embodied not only the characteristics of the small-world and scale-free,but also the characteristics of dynamic self-similar k_(c)-center network.The experimental results were verified by comparing the real data with the experimental data.The results showed that there are dynamic self-similar k_(c)-center networks and their internal network relationship dynamics in the micro scale,meso scale and global perspective based on information dissemination.
基金supported by the National Natural Science Foundation of China under Grant Nos.62273201 and 62103232the research fund for the Taishan Scholar Project of Shandong Province of China under Grant No.tstp20221103the Natural Science Foundation of Shandong Province under Grant No.ZR2021QF005。
文摘This paper investigates the networked evolutionary games(NEGs)with profile-dependent delays,including modeling and stability analysis.Profile-dependent delay,which varies with the game profiles,slows the information transmission between participants.Firstly,the dynamics model is proposed for the profile-dependent delayed NEG,then the algebraic formulation is established using the algebraic state space approach.Secondly,the dynamic behavior of the game is discussed,involving general stability and evolutionarily stable profile analysis.Necessary and sufficient criteria are derived using the matrices,which can be easily verified by mathematical software.Finally,a numerical example is carried out to demonstrate the validity of the theoretical results.
基金This work was partially supported by National Natural Science Foundation of China (Nos. 61273013, 61333001, 61104065, 61322307).
文摘In this paper a comprehensive introduction for modeling and control of networked evolutionary games (NEGs) via semi-tensor product (STP) approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients: network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i) undirected graph for symmetric games; ii) directed graph for asymmetric games, and iii) d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games (FEGs) are discussed, which are i) two strategies and symmetric (S-2); ii) two strategies and asymmetric (A-2); and iii) three strategies and symmetric (S-3). Three strategy updating rules (SUR) are introduced, which are i) Unconditional Imitation (UI); ii) Fermi Rule(FR); iii) Myopic Best Response Adjustment Rule (MBRA). First, we review the fundamental evolutionary equation (FEE) and use it to construct network profile dynamics (NPD)of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation (FEE) of each player is discussed. Using FEEs, the network strategy profile dynamics (NSPD) is built by providing efficient algorithms. Finally, we consider three more complicated NEGs: i) NEG with different length historical information, ii) NEG with multi-species, and iii) NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.
基金supported partly by National Natural Science Foundation of China(Nos.61074114 and 61273013)
文摘This paper considers the modeling and convergence of hyper-networked evolutionary games (HNEGs). In an HNEG the network graph is a hypergraph, which allows the fundamental network game to be a multi-player one. Using semi-tensor product of matrices and the fundamental evolutionary equation, the dynamics of an HNEG is obtained and we extend the results about the networked evolutionary games to show whether an HNEG is potential and how to calculate the potential. Then we propose a new strategy updating rule, called the cascading myopic best response adjustment rule (MBRAR), and prove that under the cascading MBRAR the strategies of an HNEG will converge to a pure Nash equilibrium. An example is presented and discussed in detail to demonstrate the theoretical and numerical results.
文摘In the present study,a novel approach based on an evolutionary wavelet neural network(EWNN)is proposed to estimate the slag quality in an electric arc furnace(EAF)employing power quality indices.In the EWNN,an evolutionary method is applied to train the parameters for a combination of neural networks and wavelets.I For this purpose,all of the electrical parameters for six melting processes are measured with a power quality analyzer,attached to the secondary component of an EAF transformer at a Saba steel complex,to estimate the foaming slag quality.Experimental results on various combinations of measured electrical parameters,applying the designed EWNN estimator,demonstrate that utilizing five leading indicators leads to the highest precision.The obtained 99%accuracy for estimating the foaming slag quality by EWNN compared to the other methods illustrates the proposed method's efficiency.
文摘Evolutionary neural network(ENN)shows high performance in function optimization and in finding approximately global optima from searching large and complex spaces.It is one of the most efficient and adaptive optimization techniques used widely to provide candidate solutions that lead to the fitness of the problem.ENN has the extraordinary ability to search the global and learning the approximate optimal solution regardless of the gradient information of the error functions.However,ENN requires high computation and processing which requires parallel processing platforms such as field programmable gate arrays(FPGAs)and graphic processing units(GPUs)to achieve a good performance.This work involves different new implementations of ENN by exploring and adopting different techniques and opportunities for parallel processing.Different versions of ENN algorithm have also been implemented and parallelized on FPGAs platform for low latency by exploiting the parallelism and pipelining approaches.Real data form mass spectrometry data(MSD)application was tested to examine and verify our implementations.This is a very important and extensive computation application which needs to search and find the optimal features(peaks)in MSD in order to distinguish cancer patients from control patients.ENN algorithm is also implemented and parallelized on single core and GPU platforms for comparison purposes.The computation time of our optimized algorithm on FPGA and GPU has been improved by a factor of 6.75 and 6,respectively.
基金Shi acknowledges financial support from the National Natural Science Foundation of China(Grant 91752202).
文摘Lacking labeled examples of working numerical strategies,adapting an iterative solver to accommodate a numerical issue,e.g.,density discontinuities in the pressure Poisson equation,is non-trivial and usually involves a lot of trial and error.Here,we resort to evolutionary neural network.A evolutionary neural network observes the outcome of an action and adapts its strategy accordingly.The process requires no labeled data but only a measure of a network’s performance at a task.Applying neuro-evolution and adapting the Jacobi iterative method for the pressure Poisson equation with density discontinuities,we show that the adapted Jacobi method is able to accommodate density discontinuities.
基金supported partly by National Natural Science Foundation(NNSF)of China,[grant numbers 61273013 and 61333001].
文摘Basic concepts about the finite potential games and the networked evolutionary games(NEGs)are introduced.Some new developments are surveyed,including(i)formulas for verifying whether a finite game is(weighted)potential and for calculating the(weighted)potential function;and(ii)the fundamental network equation and strategy profile dynamics of NEGs.Then some applications are introduced,which include:(i)convergence of NEGs;(ii)congestion control;(iii)distributed coverage of graphs.
基金supported by the National Natural Science Foundation of China under Grant No.71371186。
文摘This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established for PTDBN with impulsive effect.Then,based on the probabilistic state transition matrix,a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive effect.Finally,the obtained new result is applied to the networked evolutionary game with memories.