With the development of smart grid, operation and control of a power system can be realized through the power communication network, especially the power production and enterprise management business involve a large a...With the development of smart grid, operation and control of a power system can be realized through the power communication network, especially the power production and enterprise management business involve a large amount of sensitive information, and the requirements for data security and real-time transmission are gradually improved. In this paper, a new 9-dimensional(9D) complex chaotic system with quaternion is proposed for the encryption of smart grid data. Firstly, we present the mathematical model of the system, and analyze its attractors, bifurcation diagram, complexity,and 0–1 test. Secondly, the pseudo-random sequences are generated by the new chaotic system to encrypt power data.Finally, the proposed encryption algorithm is verified with power data and images in the smart grid, which can ensure the encryption security and real time. The verification results show that the proposed encryption scheme is technically feasible and available for power data and image encryption in smart grid.展开更多
In this paper, structure identification of an uncertain network coupled with complex-variable chaotic systems is in- vestigated. Both the topological structure and the system parameters can be unknown and need to be i...In this paper, structure identification of an uncertain network coupled with complex-variable chaotic systems is in- vestigated. Both the topological structure and the system parameters can be unknown and need to be identified. Based on impulsive stability theory and the Lyapunov function method, an impulsive control scheme combined with an adaptive strategy is adopted to design effective and universal network estimators. The restriction on the impulsive interval is relaxed by adopting an adaptive strategy. Further, the proposed method can monitor the online switching topology effectively. Several numerical simulations are provided to illustrate the effectiveness of the theoretical results.展开更多
The complexities of multi-wing chaotic systems based on the modified Chen system and a multi-segment quadratic function are investigated by employing the statistical complexity measure （SCM） and the spectral entropy...The complexities of multi-wing chaotic systems based on the modified Chen system and a multi-segment quadratic function are investigated by employing the statistical complexity measure （SCM） and the spectral entropy （SE） algorithm. How to choose the parameters of the SCM and SE algorithms is discussed. The results show that the complexity of the multi-wing chaotic system does not increase as the number of wings increases, and it is consistent with the results of the Grassberger-Procaccia （GP） algorithm and the largest Lyapunov exponent （LLE） of the multi-wing chaotic system.展开更多
Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with...Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV展开更多
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve fini...This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lu¨ and Chen systems are presented to validate the design and analysis.展开更多
The aim of this paper is to study complex modified projective synchronization（CMPS） between fractional-order chaotic nonlinear systems with incommensurate orders. Based on the stability theory of incommensurate frac...The aim of this paper is to study complex modified projective synchronization（CMPS） between fractional-order chaotic nonlinear systems with incommensurate orders. Based on the stability theory of incommensurate fractional-order systems and active control method, control laws are derived to achieve CMPS in three situations including fractional-order complex Lorenz system driving fractional-order complex Chen system, fractional-order real Rssler system driving fractional-order complex Chen system, and fractionalorder complex Lorenz system driving fractional-order real Lü system. Numerical simulations confirm the validity and feasibility of the analytical method.展开更多
Explosive synchronization (ES), as one kind of abrupt dynamical transitions in nonlinearly coupled systems, has become a hot spot of modern complex networks. At present, many results of ES are based on the networked K...Explosive synchronization (ES), as one kind of abrupt dynamical transitions in nonlinearly coupled systems, has become a hot spot of modern complex networks. At present, many results of ES are based on the networked Kuramoto oscillators and little attention has been paid to the influence of chaotic dynamics on synchronization transitions. Here, the unified chaotic systems (Lorenz, Lü and Chen) and R?ssler systems are studied to report evidence of an explosive synchronization of chaotic systems with different topological network structures. The results show that ES is clearly observed in coupled Lorenz systems. However, the continuous transitions take place in the coupled Chen and Lü systems, even though a big shock exits during the synchronization process. In addition, the coupled R?ssler systems will keep synchronous once the entire network is completely synchronized, although the coupling strength is reduced. Finally, we give some explanations from the dynamical features of the unified chaotic systems and the periodic orbit of the R?ssler systems.展开更多
Complex networks are important paradigms for analyzing the complex systems as they allow understanding the structural properties of systems composed of different interacting entities. In this work we propose a reliabl...Complex networks are important paradigms for analyzing the complex systems as they allow understanding the structural properties of systems composed of different interacting entities. In this work we propose a reliable method for constructing complex networks from chaotic time series. We first estimate the covariance matrices, then a geodesic-based distance between the covariance matrices is introduced. Consequently the network can be constructed on a Riemannian manifold where the nodes and edges correspond to the covariance matrix and geodesic-based distance, respectively. The proposed method provides us with an intrinsic geometry viewpoint to understand the time series.展开更多
The stabilization properties of various typical complex dynamical networks composed of chaotic nodes are theoretically investigated and numerically simulated in detail. Some local stability properties of such pinned n...The stabilization properties of various typical complex dynamical networks composed of chaotic nodes are theoretically investigated and numerically simulated in detail. Some local stability properties of such pinned networks are derived and the valid stability regions are estimated based on eigenvalue analysis. Numerical simulations of such networks are given to explain why significantly less local controllers are needed by the specifically pinning scheme, which pins the most highly connected nodes in scale-free networks, than that required by the randomly pinning scheme. Also, it is explained why there is no significant difference between the two schemes for controlling random-graph networks and small-world networks.展开更多
To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where...To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.展开更多
Nonlinear systems involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems, for example, many biological phenomena involving thresholds, bursting rhythm...Nonlinear systems involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems, for example, many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, population dynamics, etc., do exhibit impulsive effects. In a recent paper [1], both real and complex Van der Pol oscillators were introduced and shown to exhibit chaotic limit cycles and in [2] an active control and chaos synchronization was introduced. In this paper, impulsive synchronization for the real and complex Van der Pol oscillators is systematically investigated. We derive analytical expressions for impulsive control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set of initial conditions, the differences between the master and slave systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.展开更多
基金Project supported by the International Collaborative Research Project of Qilu University of Technology (Grant No.QLUTGJHZ2018020)the Project of Youth Innovation and Technology Support Plan for Colleges and Universities in Shandong Province,China (Grant No.2021KJ025)the Major Scientific and Technological Innovation Projects of Shandong Province,China (Grant Nos.2019JZZY010731 and 2020CXGC010901)。
文摘With the development of smart grid, operation and control of a power system can be realized through the power communication network, especially the power production and enterprise management business involve a large amount of sensitive information, and the requirements for data security and real-time transmission are gradually improved. In this paper, a new 9-dimensional(9D) complex chaotic system with quaternion is proposed for the encryption of smart grid data. Firstly, we present the mathematical model of the system, and analyze its attractors, bifurcation diagram, complexity,and 0–1 test. Secondly, the pseudo-random sequences are generated by the new chaotic system to encrypt power data.Finally, the proposed encryption algorithm is verified with power data and images in the smart grid, which can ensure the encryption security and real time. The verification results show that the proposed encryption scheme is technically feasible and available for power data and image encryption in smart grid.
基金Project supported by the Tianyuan Special Funds of the National Natural Science Foundation of China(Grant No.11226242)the Natural Science Foundation of Jiangxi Province of China(Grant No.20122BAB211006)
文摘In this paper, structure identification of an uncertain network coupled with complex-variable chaotic systems is in- vestigated. Both the topological structure and the system parameters can be unknown and need to be identified. Based on impulsive stability theory and the Lyapunov function method, an impulsive control scheme combined with an adaptive strategy is adopted to design effective and universal network estimators. The restriction on the impulsive interval is relaxed by adopting an adaptive strategy. Further, the proposed method can monitor the online switching topology effectively. Several numerical simulations are provided to illustrate the effectiveness of the theoretical results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61161006 and 61073187)
文摘The complexities of multi-wing chaotic systems based on the modified Chen system and a multi-segment quadratic function are investigated by employing the statistical complexity measure （SCM） and the spectral entropy （SE） algorithm. How to choose the parameters of the SCM and SE algorithms is discussed. The results show that the complexity of the multi-wing chaotic system does not increase as the number of wings increases, and it is consistent with the results of the Grassberger-Procaccia （GP） algorithm and the largest Lyapunov exponent （LLE） of the multi-wing chaotic system.
基金Project supported by the National Natural Science Foundation of China （Grant No 10172056）, the Natural Science Foundation of Zhejiang Province, China （Grant No Y604106）, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, the Scientific Research Foundation of Zhejiang Provincial Education Department of China （Grant No 20070568） and the Natural Science Foundation of Zhejiang Lishui University （Grant No KZ04008）.
文摘Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for a general （2＋1）-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system （GKdV） is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV
基金the National Natural Science Foundation of China(Grant Nos.60874009 and 10971120)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2010FM010)
文摘This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lu¨ and Chen systems are presented to validate the design and analysis.
基金supported by Key Program of National Natural Science Foundation of China (No. 61533011)National Natural Science Foundation of China (Nos. 61273088 and 61603203)
文摘The aim of this paper is to study complex modified projective synchronization（CMPS） between fractional-order chaotic nonlinear systems with incommensurate orders. Based on the stability theory of incommensurate fractional-order systems and active control method, control laws are derived to achieve CMPS in three situations including fractional-order complex Lorenz system driving fractional-order complex Chen system, fractional-order real Rssler system driving fractional-order complex Chen system, and fractionalorder complex Lorenz system driving fractional-order real Lü system. Numerical simulations confirm the validity and feasibility of the analytical method.
文摘Explosive synchronization (ES), as one kind of abrupt dynamical transitions in nonlinearly coupled systems, has become a hot spot of modern complex networks. At present, many results of ES are based on the networked Kuramoto oscillators and little attention has been paid to the influence of chaotic dynamics on synchronization transitions. Here, the unified chaotic systems (Lorenz, Lü and Chen) and R?ssler systems are studied to report evidence of an explosive synchronization of chaotic systems with different topological network structures. The results show that ES is clearly observed in coupled Lorenz systems. However, the continuous transitions take place in the coupled Chen and Lü systems, even though a big shock exits during the synchronization process. In addition, the coupled R?ssler systems will keep synchronous once the entire network is completely synchronized, although the coupling strength is reduced. Finally, we give some explanations from the dynamical features of the unified chaotic systems and the periodic orbit of the R?ssler systems.
基金Supported by the National Natural Science Foundation of China under Grant No 61362024
文摘Complex networks are important paradigms for analyzing the complex systems as they allow understanding the structural properties of systems composed of different interacting entities. In this work we propose a reliable method for constructing complex networks from chaotic time series. We first estimate the covariance matrices, then a geodesic-based distance between the covariance matrices is introduced. Consequently the network can be constructed on a Riemannian manifold where the nodes and edges correspond to the covariance matrix and geodesic-based distance, respectively. The proposed method provides us with an intrinsic geometry viewpoint to understand the time series.
基金the National Natural Science Foundation of China (No.60774088, 60504017)the Specialized Research Fund for theDoctoral Program of Higher Education of China (No.20050055013)the Program for New Century Excellent Talents of China (NCET)
文摘The stabilization properties of various typical complex dynamical networks composed of chaotic nodes are theoretically investigated and numerically simulated in detail. Some local stability properties of such pinned networks are derived and the valid stability regions are estimated based on eigenvalue analysis. Numerical simulations of such networks are given to explain why significantly less local controllers are needed by the specifically pinning scheme, which pins the most highly connected nodes in scale-free networks, than that required by the randomly pinning scheme. Also, it is explained why there is no significant difference between the two schemes for controlling random-graph networks and small-world networks.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61273088,10971120,and 61001099)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2010FM010)
文摘To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.
文摘Nonlinear systems involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems, for example, many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, population dynamics, etc., do exhibit impulsive effects. In a recent paper [1], both real and complex Van der Pol oscillators were introduced and shown to exhibit chaotic limit cycles and in [2] an active control and chaos synchronization was introduced. In this paper, impulsive synchronization for the real and complex Van der Pol oscillators is systematically investigated. We derive analytical expressions for impulsive control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set of initial conditions, the differences between the master and slave systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.
