In this paper, the coupling function of the complex dynamical networks was generalized, and the conditions for the stability of synchronization were given. We illustrate the impact of coupling function on the synchron...In this paper, the coupling function of the complex dynamical networks was generalized, and the conditions for the stability of synchronization were given. We illustrate the impact of coupling function on the synchronization of complex dynamical networks, that is, the coupling strength can not assure the stability of synchronization when the coupling function is linear. However we can modulate coupling function to achieve stability of synchronization without changing coupling strength.展开更多
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often ...Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.展开更多
This paper proposes a new impulsive complex delayed dynamical network model with output coupling, which is totally different from some existing network models. Then, by employing impulsive delay differential inequalit...This paper proposes a new impulsive complex delayed dynamical network model with output coupling, which is totally different from some existing network models. Then, by employing impulsive delay differential inequalities, some sufficient conditions are obtained to guarantee the global exponential state synchronization and output synchronization of the impulsive complex delayed dynamical network. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.展开更多
In this paper,the fixed-time outer synchronization of complex networks with noise coupling is investigated.Based on the theory of fixed-time stability and matrix inequalities,sufficient conditions for fixed-time outer...In this paper,the fixed-time outer synchronization of complex networks with noise coupling is investigated.Based on the theory of fixed-time stability and matrix inequalities,sufficient conditions for fixed-time outer synchronization are established and the estimation of the upper bound of the setting time is obtained.The result shows that the setting time can be adjusted to a desired value regardless of the initial states.Numerical simulations are performed to verify the effectiveness of the theoretical results.The effects of control parameters and the density of controlled nodes on the converging time are studied.展开更多
This paper mainly investigates the exponential synchronization of an inner time-varying complex network with coupling delay. Firstly, the synchronization of complex networks is decoupled into the stability of the corr...This paper mainly investigates the exponential synchronization of an inner time-varying complex network with coupling delay. Firstly, the synchronization of complex networks is decoupled into the stability of the corresponding dynamical systems. Based on the Lyapunov function theory, some sufficient conditions to guarantee its stability with any given convergence rate are derived, thus the synchronization of the networks is achieved. Finally, the results are illustrated by a simple time-varying network model with a coupling delay. All involved numerical simulations verify the correctness of the theoretical analysis.展开更多
We deal with the problem of pinning sampled-data synchronization for a complex network with probabilistic time-varying coupling delay. The sampling period considered here is assumed to be less than a given bound. With...We deal with the problem of pinning sampled-data synchronization for a complex network with probabilistic time-varying coupling delay. The sampling period considered here is assumed to be less than a given bound. Without using the Kronecker product, a new synchronization error system is constructed by using the property of the random variable and input delay approach. Based on the Lyapunov theory, a delay-dependent pinning sampled-data synchronization criterion is derived in terms of linear matrix inequalities （LMIs） that can be solved effectively by using MATLAB LMI toolbox. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.展开更多
The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory...The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat＇s lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.展开更多
In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous...In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule and the linear matrix inequality （LMI） optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.展开更多
In this paper, the H∞ synchronization is intensively investigated for general delayed complex dynamical networks. The network under consideration contains unknown but bounded nonlinear coupling functions, time-varyin...In this paper, the H∞ synchronization is intensively investigated for general delayed complex dynamical networks. The network under consideration contains unknown but bounded nonlinear coupling functions, time-varying delay, external distur- bances, and lt6-type stochastic disturbances, which is a zero-mean real scalar Wiener process. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule, and linear matrix inequality （LMI） optimization technique, some delay-dependent H∞ synchro- nization schemes are established, which guarantee robust stochas- tically mean square asymptotically synchronization for drive net- work and noise-perturbed response network as well as achieving a prescribed stochastic robust H∞ performance level. Finally, de- tailed and satisfactory numerical results have validated the feasi- bility and the correctness of the proposed techniques.展开更多
This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 ...This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 〈 q 〈 1 is obtained based on the stability theory of the fractional-order system. The control method which combines active control with pinning control is then suggested to obtain the controllers. Furthermore, the adaptive strategy is applied to tune the control gains and coupling strength. Corresponding numerical simulations are performed to verify and illustrate the theoretical results.展开更多
This paper deals with the modified function projective synchronization problem for general complex networks with multiple proportional delays. With the existence of multiple proportional delays, an effective hybrid fe...This paper deals with the modified function projective synchronization problem for general complex networks with multiple proportional delays. With the existence of multiple proportional delays, an effective hybrid feedback control is designed to attain modified function projective synchronization of networks. Numerical example is provided to show the effectiveness of our result.展开更多
This paper mainly investigates the finite-time and fixed-time synchronization problem for a class of general output-coupling complex networks with output feedback nodes. The fixed-time and finite-time synchronization ...This paper mainly investigates the finite-time and fixed-time synchronization problem for a class of general output-coupling complex networks with output feedback nodes. The fixed-time and finite-time synchronization protocols are presented based on continuous controller strategies which can efficaciously eliminate chattering phenomenon existing in some previous results. Several sufficient conditions ensuring fixed-time and finite-time synchronization are derived by employing Lyapunov stability theory, linear matrix inequality (LMI) and adaptive technique. Furthermore, aimed at the model of this article, we study the problem of adaptive coupling strength in fixed-time synchronization which is rarely involved in previous results. Finally, several numerical examples are given to illustrate the effectiveness of our results.展开更多
This paper focuses on synchronization of fractionalorder complex dynamical networks with decentralized adaptive coupling.Based on local information among neighboring nodes,two fractional-order decentralized adaptive s...This paper focuses on synchronization of fractionalorder complex dynamical networks with decentralized adaptive coupling.Based on local information among neighboring nodes,two fractional-order decentralized adaptive strategies are designed to tune all or only a small fraction of the coupling gains respectively.By constructing quadratic Lyapunov functions and utilizing fractional inequality techniques,Mittag-Leffler function,and Laplace transform,two sufficient conditions are derived for reaching network synchronization by using the proposed adaptive laws.Finally,two numerical examples are given to verify the theoretical results.展开更多
We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node. Both delay coupling and non-delay coupling, as well as the symmetrical coupling matrix and the asymmetrical coupli...We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node. Both delay coupling and non-delay coupling, as well as the symmetrical coupling matrix and the asymmetrical coupling matrix are considered. Based on the comparison theorem of an impulsive differential system, some novel synchronization criteria are derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.展开更多
The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the...The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.展开更多
This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simpl...This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems. Then, both the general intermittent networked controller and the quantized parameters can be designed, which guarantee that the nodes of the complex network are synchronized. Finally, simulation examples are given to illustrate the effectiveness and feasibility of the proposed method.展开更多
We investigate the problem of function projective synchronization （FPS） in drive–response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks wi...We investigate the problem of function projective synchronization （FPS） in drive–response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks with uncertain parameters and disturbance. Not only are the unknown parameters of the networks estimated by the adaptive laws obtained from the Lyapunov stability theory and Taylor expansions, but the unknown bounded disturbances are also simultaneously conquered by the proposed control. Finally, a numerical simulation is provided to illustrate the feasibility and effectiveness of the obtained result.展开更多
In this paper, by using both the linear stability analysis and Lyapunov function approach, some conditions for stabilizing synchronization behavior in a discrete-time complex dynamical network were derived. These cond...In this paper, by using both the linear stability analysis and Lyapunov function approach, some conditions for stabilizing synchronization behavior in a discrete-time complex dynamical network were derived. These conditions were determined by the coupling strength and the eigenvalues of coupling configuration matrix. Furthermore, some explicit results were obtained when the coupling map between the nodes is equal to the dynamics function of the network, which implies that the product of the coupling strength and the eigenvalues is bounded.展开更多
This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown co...This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.展开更多
The human brain is the most complicated and fascinated system and executes various important brain functions, but its underlying mechanism is a long-standing problem. In recent years, based on the progress of complex ...The human brain is the most complicated and fascinated system and executes various important brain functions, but its underlying mechanism is a long-standing problem. In recent years, based on the progress of complex network science, much attention has been paid to this problem and many important results have been achieved, thus it is the time to make a summary to help further studies. For this purpose, we here make a brief but comprehensive review on those results from the aspect of brain networks, i.e., from the angle of synchronization and complex network. First, we briefly discuss the main features of human brain and its cognitive functions through synchronization. Then, we discuss how to construct both the anatomical and functional brain networks, including the pathological brain networks such as epilepsy and Alzheimer’s diseases. Next, we discuss the approaches of studying brain networks. After that, we discuss the current progress of understanding the mechanisms of brain functions, including the aspects of chimera state, remote synchronization, explosive synchronization, intelligence quotient, and remote propagation. Finally, we make a brief discussion on the envision of future study.展开更多
基金Project supported by National Natural Science Foundation of China (Grant No .10471087) ,and Science Foundation of Shang-hai Municipal Commission of Education (Grant No .03AK33)
文摘In this paper, the coupling function of the complex dynamical networks was generalized, and the conditions for the stability of synchronization were given. We illustrate the impact of coupling function on the synchronization of complex dynamical networks, that is, the coupling strength can not assure the stability of synchronization when the coupling function is linear. However we can modulate coupling function to achieve stability of synchronization without changing coupling strength.
基金supported by National Natural Science Foundation of China under Nos. 10702023 and 10832006China Post-doctoral Special Science Foundation No. 200801020+1 种基金the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No. 2007110020110supported in part by the Project of Knowledge Innovation Program (PKIP) of Chinese Academy of Sciences
文摘Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.
基金supported by Key Project of Chinese Education Ministry(No.212138)Natural Science Foundation of Chongqing(No.CQ CSTC2011BB0117)+1 种基金Foundation of Science and Technology Project of Chongqing Education Commission(No.KJ120630)Innovation Foundation of BUAA for PhD Graduates(No.YWF-12-RBYJ-005)
文摘This paper proposes a new impulsive complex delayed dynamical network model with output coupling, which is totally different from some existing network models. Then, by employing impulsive delay differential inequalities, some sufficient conditions are obtained to guarantee the global exponential state synchronization and output synchronization of the impulsive complex delayed dynamical network. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11711530203 and 11771443the Fundamental Research Funds for the Central Universities under Grant No.2015XKMS076
文摘In this paper,the fixed-time outer synchronization of complex networks with noise coupling is investigated.Based on the theory of fixed-time stability and matrix inequalities,sufficient conditions for fixed-time outer synchronization are established and the estimation of the upper bound of the setting time is obtained.The result shows that the setting time can be adjusted to a desired value regardless of the initial states.Numerical simulations are performed to verify the effectiveness of the theoretical results.The effects of control parameters and the density of controlled nodes on the converging time are studied.
基金supported in part by the National Natural Science Foundation of China (Grant No. 11047114)the Key Project of the Chinese Ministry of Education (Grant No. 210141)the Youth Foundation of the Educational Committee of Hubei Province of China (Grant Nos. Q20111607 and Q20111611)
文摘This paper mainly investigates the exponential synchronization of an inner time-varying complex network with coupling delay. Firstly, the synchronization of complex networks is decoupled into the stability of the corresponding dynamical systems. Based on the Lyapunov function theory, some sufficient conditions to guarantee its stability with any given convergence rate are derived, thus the synchronization of the networks is achieved. Finally, the results are illustrated by a simple time-varying network model with a coupling delay. All involved numerical simulations verify the correctness of the theoretical analysis.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61203049 and 61303020)the Natural Science Foundation of Shanxi Province of China(Grant No.2013021018-3)the Doctoral Startup Foundation of Taiyuan University of Science and Technology,China(Grant No.20112010)
文摘We deal with the problem of pinning sampled-data synchronization for a complex network with probabilistic time-varying coupling delay. The sampling period considered here is assumed to be less than a given bound. Without using the Kronecker product, a new synchronization error system is constructed by using the property of the random variable and input delay approach. Based on the Lyapunov theory, a delay-dependent pinning sampled-data synchronization criterion is derived in terms of linear matrix inequalities （LMIs） that can be solved effectively by using MATLAB LMI toolbox. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.
文摘The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat＇s lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.
基金supported by the National Natural Science Foundation of China (Grant No. 60904060)the Open Foundation of Hubei Province Key Laboratory of Systems Science in Metallurgical Process,China (Grant No. C201010)
文摘In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule and the linear matrix inequality （LMI） optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.
基金Supported by the National Natural Science Foundation of China(6090406061104127)
文摘In this paper, the H∞ synchronization is intensively investigated for general delayed complex dynamical networks. The network under consideration contains unknown but bounded nonlinear coupling functions, time-varying delay, external distur- bances, and lt6-type stochastic disturbances, which is a zero-mean real scalar Wiener process. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule, and linear matrix inequality （LMI） optimization technique, some delay-dependent H∞ synchro- nization schemes are established, which guarantee robust stochas- tically mean square asymptotically synchronization for drive net- work and noise-perturbed response network as well as achieving a prescribed stochastic robust H∞ performance level. Finally, de- tailed and satisfactory numerical results have validated the feasi- bility and the correctness of the proposed techniques.
文摘This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 〈 q 〈 1 is obtained based on the stability theory of the fractional-order system. The control method which combines active control with pinning control is then suggested to obtain the controllers. Furthermore, the adaptive strategy is applied to tune the control gains and coupling strength. Corresponding numerical simulations are performed to verify and illustrate the theoretical results.
文摘This paper deals with the modified function projective synchronization problem for general complex networks with multiple proportional delays. With the existence of multiple proportional delays, an effective hybrid feedback control is designed to attain modified function projective synchronization of networks. Numerical example is provided to show the effectiveness of our result.
文摘This paper mainly investigates the finite-time and fixed-time synchronization problem for a class of general output-coupling complex networks with output feedback nodes. The fixed-time and finite-time synchronization protocols are presented based on continuous controller strategies which can efficaciously eliminate chattering phenomenon existing in some previous results. Several sufficient conditions ensuring fixed-time and finite-time synchronization are derived by employing Lyapunov stability theory, linear matrix inequality (LMI) and adaptive technique. Furthermore, aimed at the model of this article, we study the problem of adaptive coupling strength in fixed-time synchronization which is rarely involved in previous results. Finally, several numerical examples are given to illustrate the effectiveness of our results.
基金supported by the"Chunhui Plan"Cooperative Research for Ministry of Education(Z2016133)the Open Research Fund of Key Laboratory of Automobile Engineering(Xihua University)+3 种基金Sichuan Province(szjj2016-017)the National Natural Science Foundation of China(51177137)the Scientific Research Foundation of the Education Department of Sichuan Province(16ZB0163)the China Scholarship Council
文摘This paper focuses on synchronization of fractionalorder complex dynamical networks with decentralized adaptive coupling.Based on local information among neighboring nodes,two fractional-order decentralized adaptive strategies are designed to tune all or only a small fraction of the coupling gains respectively.By constructing quadratic Lyapunov functions and utilizing fractional inequality techniques,Mittag-Leffler function,and Laplace transform,two sufficient conditions are derived for reaching network synchronization by using the proposed adaptive laws.Finally,two numerical examples are given to verify the theoretical results.
基金Project supported by the Young Project of Hubei Provincial Department of Education,China(Grant No.Q20111309)the Key Program of Hubei Provincial Department of Education,China(Grant No.D20101304)
文摘We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node. Both delay coupling and non-delay coupling, as well as the symmetrical coupling matrix and the asymmetrical coupling matrix are considered. Based on the comparison theorem of an impulsive differential system, some novel synchronization criteria are derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.
基金supported by National Natural Science Foundation of China(No.61273008)Science Research Project of Liaoning Provicial Education Department(No.L2012208)Science Foundation of Ministry of Housing and Urban-Rural Development(No.2013-K5-2)
文摘The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.
文摘This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems. Then, both the general intermittent networked controller and the quantized parameters can be designed, which guarantee that the nodes of the complex network are synchronized. Finally, simulation examples are given to illustrate the effectiveness and feasibility of the proposed method.
基金the National Natural Science Foundation of China(Grant No.70871056)the Fundamental Research Funds for the Central Universities,China(Grant No.2013B10014)
文摘We investigate the problem of function projective synchronization （FPS） in drive–response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks with uncertain parameters and disturbance. Not only are the unknown parameters of the networks estimated by the adaptive laws obtained from the Lyapunov stability theory and Taylor expansions, but the unknown bounded disturbances are also simultaneously conquered by the proposed control. Finally, a numerical simulation is provided to illustrate the feasibility and effectiveness of the obtained result.
基金Project supported by the National Natural Science Foundation of China （Grant No.10471087）, and Science Foundation of Shanghai Municipal Commission of Education （Grant No.03AK33）
文摘In this paper, by using both the linear stability analysis and Lyapunov function approach, some conditions for stabilizing synchronization behavior in a discrete-time complex dynamical network were derived. These conditions were determined by the coupling strength and the eigenvalues of coupling configuration matrix. Furthermore, some explicit results were obtained when the coupling map between the nodes is equal to the dynamics function of the network, which implies that the product of the coupling strength and the eigenvalues is bounded.
文摘This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.
基金This work was partially supported by the National Natural Science Foundation of China under Grant Nos.11835003,82161148012,and 12175070the"Technology Innovation 2030-major Projects"on brain science and brain-like computing of the Ministry of Science&Tecknology of China(No.2021ZD0202600).
文摘The human brain is the most complicated and fascinated system and executes various important brain functions, but its underlying mechanism is a long-standing problem. In recent years, based on the progress of complex network science, much attention has been paid to this problem and many important results have been achieved, thus it is the time to make a summary to help further studies. For this purpose, we here make a brief but comprehensive review on those results from the aspect of brain networks, i.e., from the angle of synchronization and complex network. First, we briefly discuss the main features of human brain and its cognitive functions through synchronization. Then, we discuss how to construct both the anatomical and functional brain networks, including the pathological brain networks such as epilepsy and Alzheimer’s diseases. Next, we discuss the approaches of studying brain networks. After that, we discuss the current progress of understanding the mechanisms of brain functions, including the aspects of chimera state, remote synchronization, explosive synchronization, intelligence quotient, and remote propagation. Finally, we make a brief discussion on the envision of future study.
