This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapun...This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov expo- nents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench （EWB）. Numerical simulations are presented to show these results.展开更多
We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies.Based on graph theory and Lyapunov stability theory,the adaptive control method is em...We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies.Based on graph theory and Lyapunov stability theory,the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations.Simulation examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.展开更多
In this paper,the modulation instability(MI),rogue waves(RWs)and conseryation laws of the coupled higher-order nonlinear Schrodinger equation are investigated.According to MI and the 2×2 Lax pair,Darboux-dressing...In this paper,the modulation instability(MI),rogue waves(RWs)and conseryation laws of the coupled higher-order nonlinear Schrodinger equation are investigated.According to MI and the 2×2 Lax pair,Darboux-dressing transformation with an asymptotic expansion method,the existence and properties of the one-,second-,and third-order RWs for the higher-order nonlinear Schrodinger equation are constructed.In addition,the main characteristics of these solutions are discussed through some graphics,which are draw widespread attention in a variety of complex systems such as optics,Bose-Einstein condensates,capillary fow,superfluidity,fluid dynamics,and finance.In addition,infinitely-many conservation laws are established.展开更多
The nonlinear Schr6dinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the dis...The nonlinear Schr6dinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.展开更多
The simple Lie point symmetry reduction procedure is used to obtain infinitely many symmetries to a new integrable system of coupled KdV equations. Using some symmetry subalgebra of the equations, five types of the si...The simple Lie point symmetry reduction procedure is used to obtain infinitely many symmetries to a new integrable system of coupled KdV equations. Using some symmetry subalgebra of the equations, five types of the significant similarity reductions are obtained by virtue of the Lie group approach, and obtain abundant solutions of the coupled KdV equations, such as the solitary wave solution, exponential solution, rational solution, polynomial solution, etc.展开更多
A new idea is put forward to modify the Clarkson-Kruskal （CK） direct method. Using the usual CK direct method to a coupled KdV system, two types of usual similarity reductions can be obtained. However, the applicati...A new idea is put forward to modify the Clarkson-Kruskal （CK） direct method. Using the usual CK direct method to a coupled KdV system, two types of usual similarity reductions can be obtained. However, the application of the modified CK direct method leads to three types of new similarity reductions different from the usual ones.展开更多
This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point,...This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.展开更多
This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor...This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.展开更多
This paper introduces an adaptive procedure for the problem of synchronization and parameter identification for chaotic networks with time-varying delay by combining adaptive control and linear feedback. In particular...This paper introduces an adaptive procedure for the problem of synchronization and parameter identification for chaotic networks with time-varying delay by combining adaptive control and linear feedback. In particular, we consider that the equations xi（t） （for i = r＋ 1, r＋2,... ,n） can be expressed by the former xi（t） （for i=1,2,...,r）, which is not the same as the previous equation. This approach is also able to track changes in the operating parameters of chaotic networks rapidly and the speed of synchronization and parameter estimation can be adjusted. In addition, this method is quite robust against the effect of slight noise and the estimated value of a parameter fluctuates around the correct value.展开更多
Cluster synchronization of nonlinear uncertain complex networks with desynchronizing impulse is explored. First of all, a feedback controller is employed, based on the Lyapunov stability theorem and Lipschitz conditio...Cluster synchronization of nonlinear uncertain complex networks with desynchronizing impulse is explored. First of all, a feedback controller is employed, based on the Lyapunov stability theorem and Lipschitz condition, to guarantee that the uncertain complex networks with desynchronizing impulse synchronize with an object trajectory. Furthermore, a synchronizing impulse controller is presented, which is more efficiently and directly used to achieve the cluster synchronization. Finally, numerical examples are examined to show the effectiveness of the proposed methods.展开更多
In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg-de Vries （KdV） equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant simila...In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg-de Vries （KdV） equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant similarity reductions. Abundant solutions of the coupled KdV equation system, such as the solitary wave solution, exponential solution, rational solution and polynomial solution, etc. are obtained from the reduced equations. Especially, one type of group-invarlant solution of reduced equations can be acquired by means of the Painlevé I transcendent function.展开更多
In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This ...In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This paper presents the comprehensive discussion of the approach and also extensive applications.展开更多
This paper is involved with the adaptive control and synchronization problems for an uncertain new hyperchaotic Lorenz system. Based on the Lyapunov stability theory, the adaptive control law is derived such that the ...This paper is involved with the adaptive control and synchronization problems for an uncertain new hyperchaotic Lorenz system. Based on the Lyapunov stability theory, the adaptive control law is derived such that the trajectory of hyperchaotic Lorenz system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. Furthermore, an adaptive control approach is presented to the synchronizations between two identical hyperchaotic systems, particularly between two different uncertain hyperchaotic systems. Numerical simulations show the effectiveness of the presented method.展开更多
In this paper,we explore the exact solutions to the fourth-order extended(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation.Based on Hirota bilinear method,lump solution,periodic cross-kink solutions and bright...In this paper,we explore the exact solutions to the fourth-order extended(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation.Based on Hirota bilinear method,lump solution,periodic cross-kink solutions and bright-dark soliton solutions were investigated.By calculating and solving,the peak and trough of lump solution are obtained,and the maximum and minimum points of each are solved.The three-dimensional plots and density plots of periodic cross-kink solution and bright-dark soliton solution are drawn and the dynamics of solutions under different parameters are observed.展开更多
This paper first investigates the projective synchronisation problem with non-delayed and delayed coupling between drive-response dynamical networks consisting of identical nodes and different nodes. Based on Lyapunov...This paper first investigates the projective synchronisation problem with non-delayed and delayed coupling between drive-response dynamical networks consisting of identical nodes and different nodes. Based on Lyapunov stability theory, several nonlinear controllers are applied to achieve the projective synchronisation between the drive-response dynamical networks; simultaneously the topological structure of the drive dynamical complex networks can be exactly identified. Moreover, numerical examples are presented to verify the feasibility and effectiveness of the theorems.展开更多
The boundary control of MKdV-Burgers equation was considered by feedback control on the domain [0,1]. The existence of the solution of MKdV-Burgers equation with the feedback control law was proved. On the base, prior...The boundary control of MKdV-Burgers equation was considered by feedback control on the domain [0,1]. The existence of the solution of MKdV-Burgers equation with the feedback control law was proved. On the base, priori estimates for the solution was given. At last, the existence of the weak solution of MKdV-Burgers equation was proved and the global-exponential and asymptotic stability of the solution of MKdV-Burgers equation was given.展开更多
Generalized projective synchronization （GPS） between two complex networks with time-varying coupling delay is investigated. Based on the Lyapunov stability theory, a nonlinear controller and adaptive updated laws ar...Generalized projective synchronization （GPS） between two complex networks with time-varying coupling delay is investigated. Based on the Lyapunov stability theory, a nonlinear controller and adaptive updated laws are designed. Feasibility of the proposed scheme is proven in theory. Moreover, two numerical examples are presented, using the energy resource system and Lü＇s system [Physica A 382 （2007） 672] as the nodes of the networks. GPS between two energy resource complex networks with time-varying coupling delay is achieved. This study can widen the application range of the generalized synchronization methods and will be instructive for the demand supply of energy resource in some regions of China.展开更多
In this paper, we give a detailed discussion about the dynamical behaviors of compact solitary waves subjected to the periodic perturbation. By using the phase portrait theory, we find one of the nonsmooth solitary wa...In this paper, we give a detailed discussion about the dynamical behaviors of compact solitary waves subjected to the periodic perturbation. By using the phase portrait theory, we find one of the nonsmooth solitary waves of the mKdV equation, namely, a compact solitary wave, to be a weak solution, which can be proved. It is shown that the compact solitary wave easily turns chaotic from the Melnikov theory. We focus on the sufficient conditions by keeping the system stable through selecting a suitable controller. Furthermore, we discuss the chaotic threshold for a perturbed system. Numerical simulations including chaotic thresholds, bifurcation diagrams, the maximum Lyapunov exponents, and phase portraits demonstrate that there exists a special frequency which has a great influence on our system; with the increase of the controller strength, chaos disappears in the perturbed system. But if the controller strength is sufficiently large, the solitary wave vibrates violently.展开更多
We investigate the synchronization problem of two colored networks via discrete control based on the Lyapunov stability theory.First,intermittent control is adopted to synchronize two edge-colored networks,and the suf...We investigate the synchronization problem of two colored networks via discrete control based on the Lyapunov stability theory.First,intermittent control is adopted to synchronize two edge-colored networks,and the suffi-cient condition connecting the control width,control period and the network topology is established for reaching synchronization.Then,an impulsive controller is designed to ensure two general colored networks in synchroniza-tion,and the relation among the impulsive interval,impulsive gain and the network topology for synchronization is also discovered.Finally,two numerical examples are provided to demonstrate and verify the theoretical results.展开更多
Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by no...Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations.展开更多
基金Project supported by the National Natural Science Foundations of China (Grant Nos. 70571030 and 90610031)the Society Science Foundation from Ministry of Education of China (Grant No. 08JA790057)the Advanced Talents’ Foundation and Student’s Foundation of Jiangsu University (Grant Nos. 07JDG054 and 07A075)
文摘This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov expo- nents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench （EWB）. Numerical simulations are presented to show these results.
基金Supported by the National Natural Science Foundation of China(No 71073071)the Social Science Foundation of Education Ministry(No 09YJA790088)the Major Program of Social Science Foundation of Jiangsu Education Office(No 2010-2-10).
文摘We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies.Based on graph theory and Lyapunov stability theory,the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations.Simulation examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.
基金This work is supported by the National Natural Science Foundation of China(Grant No.71690242,No.11731014,No.12001241)the Basic Research Program of Jiangsu Province(Grant No.BK20200885).
文摘In this paper,the modulation instability(MI),rogue waves(RWs)and conseryation laws of the coupled higher-order nonlinear Schrodinger equation are investigated.According to MI and the 2×2 Lax pair,Darboux-dressing transformation with an asymptotic expansion method,the existence and properties of the one-,second-,and third-order RWs for the higher-order nonlinear Schrodinger equation are constructed.In addition,the main characteristics of these solutions are discussed through some graphics,which are draw widespread attention in a variety of complex systems such as optics,Bose-Einstein condensates,capillary fow,superfluidity,fluid dynamics,and finance.In addition,infinitely-many conservation laws are established.
基金Project supported by the National Natural Science Foundation of China (Grant No.11101191)
文摘The nonlinear Schr6dinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.
基金The project supported by National Natural Science Foundation of China under Grant No. 10071033 and the Natural Science Foundation of Jiangsu Province under Grant No. BK2002003. Acknowledgments 0ne of the authors （S.P. Qian） is indebted to Prof. S.Y. Lou for his helpful discussions.
文摘The simple Lie point symmetry reduction procedure is used to obtain infinitely many symmetries to a new integrable system of coupled KdV equations. Using some symmetry subalgebra of the equations, five types of the significant similarity reductions are obtained by virtue of the Lie group approach, and obtain abundant solutions of the coupled KdV equations, such as the solitary wave solution, exponential solution, rational solution, polynomial solution, etc.
文摘A new idea is put forward to modify the Clarkson-Kruskal （CK） direct method. Using the usual CK direct method to a coupled KdV system, two types of usual similarity reductions can be obtained. However, the application of the modified CK direct method leads to three types of new similarity reductions different from the usual ones.
基金Project supported by the National Natural Science Foundations of China(Grant No.70871056)the Society Science Foundation from Ministry of Education of China(Grant No.08JA790057)the Advanced Talents'Foundation and Student's Foundation of Jiangsu University,China(Grant Nos.07JDG054 and 07A075)
文摘This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.
基金Project supported by the National Natural Science Foundations of China (Grant Nos 70571030 and 90610031)the Advanced Talents’ Foundation of Jiangsu University of China (Grant No 07JDG054)
文摘This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.70571030 and 90610031)the Social Science Foundation from Ministry of Education of China (Grant No.08JA790057)the Advanced Talents' Foundation and Student's Foundation of Jiangsu University (Grant Nos.07JDG054 and 07A075)
文摘This paper introduces an adaptive procedure for the problem of synchronization and parameter identification for chaotic networks with time-varying delay by combining adaptive control and linear feedback. In particular, we consider that the equations xi（t） （for i = r＋ 1, r＋2,... ,n） can be expressed by the former xi（t） （for i=1,2,...,r）, which is not the same as the previous equation. This approach is also able to track changes in the operating parameters of chaotic networks rapidly and the speed of synchronization and parameter estimation can be adjusted. In addition, this method is quite robust against the effect of slight noise and the estimated value of a parameter fluctuates around the correct value.
基金Project supported by the National Natural Science foundation of China(Grant Nos.51276081 and 11326193)the Students’ Research Foundation of Jiangsu University,China(Grant Nos.Y13A127 and 12A415)
文摘Cluster synchronization of nonlinear uncertain complex networks with desynchronizing impulse is explored. First of all, a feedback controller is employed, based on the Lyapunov stability theorem and Lipschitz condition, to guarantee that the uncertain complex networks with desynchronizing impulse synchronize with an object trajectory. Furthermore, a synchronizing impulse controller is presented, which is more efficiently and directly used to achieve the cluster synchronization. Finally, numerical examples are examined to show the effectiveness of the proposed methods.
基金Project supported by the National Natural Science Foundation of China （Grant No 10071033）, the Natural Science Foundation of Jiangsu Province, China （Grant No BK2002003）, and the Technology Innovation Plan for Postgraduate of Jiangsu Province in 2006 （Grant No 72）.Acknowledgment 0ne of the authors （Qian S P） is indebted to Professor Lou S Y for his helpful discussion.
文摘In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg-de Vries （KdV） equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant similarity reductions. Abundant solutions of the coupled KdV equation system, such as the solitary wave solution, exponential solution, rational solution and polynomial solution, etc. are obtained from the reduced equations. Especially, one type of group-invarlant solution of reduced equations can be acquired by means of the Painlevé I transcendent function.
基金Project supported by the National Natural Science Foundations of China (Grant Nos. 70571030 and 90610031)the Society Science Foundation from Ministry of Education of China (Grant No. 08JA790057)the Advanced Talents’ Foundation and Student’s Foundation of Jiangsu University (Grant Nos. 07JDG054 and 07A075)
文摘In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This paper presents the comprehensive discussion of the approach and also extensive applications.
基金supported by the National Natural Science Foundation of China (Grant Nos 70571030 and 90610031)the Advanced Talent Foundation of Jiangsu University of China (Grant No 07JDG054)
文摘This paper is involved with the adaptive control and synchronization problems for an uncertain new hyperchaotic Lorenz system. Based on the Lyapunov stability theory, the adaptive control law is derived such that the trajectory of hyperchaotic Lorenz system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. Furthermore, an adaptive control approach is presented to the synchronizations between two identical hyperchaotic systems, particularly between two different uncertain hyperchaotic systems. Numerical simulations show the effectiveness of the presented method.
基金the National Natural Science Foundation of China(No.11731014)。
文摘In this paper,we explore the exact solutions to the fourth-order extended(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation.Based on Hirota bilinear method,lump solution,periodic cross-kink solutions and bright-dark soliton solutions were investigated.By calculating and solving,the peak and trough of lump solution are obtained,and the maximum and minimum points of each are solved.The three-dimensional plots and density plots of periodic cross-kink solution and bright-dark soliton solution are drawn and the dynamics of solutions under different parameters are observed.
基金supported by the National Natural Science Foundation of China (Grant No. 10771088)Natural Science Foundation of Jiangsu Province,China (Grant No. 2007098)+3 种基金Outstanding Personnel Program in Six Fields of Jiangsu Province,China (Grant No. 6-A-029)National Natural Science (Youth) Foundation of China (Grant No. 10801140)Youth Foundation of Chongqing Normal University,China (Grant No. 08XLQ04)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. CX09B 202Z)
文摘This paper first investigates the projective synchronisation problem with non-delayed and delayed coupling between drive-response dynamical networks consisting of identical nodes and different nodes. Based on Lyapunov stability theory, several nonlinear controllers are applied to achieve the projective synchronisation between the drive-response dynamical networks; simultaneously the topological structure of the drive dynamical complex networks can be exactly identified. Moreover, numerical examples are presented to verify the feasibility and effectiveness of the theorems.
基金Project supported by the National Natural Science Foundation of China(No.10071033)the Natural Science Foundation of Jiangsu Province(No.BK2002003)
文摘The boundary control of MKdV-Burgers equation was considered by feedback control on the domain [0,1]. The existence of the solution of MKdV-Burgers equation with the feedback control law was proved. On the base, priori estimates for the solution was given. At last, the existence of the weak solution of MKdV-Burgers equation was proved and the global-exponential and asymptotic stability of the solution of MKdV-Burgers equation was given.
基金Supported by the National Natural Science Foundation of China under Grant No 90610031, Jiangsu Planned Projects for Postdoctoral Research Funds （No 0701038C）, the Natural Science Foundation of Jiangsu University （No 06JDG044）, and the Social Science Foundation of Jiangsu Province （No 07SJD790003）.
文摘Generalized projective synchronization （GPS） between two complex networks with time-varying coupling delay is investigated. Based on the Lyapunov stability theory, a nonlinear controller and adaptive updated laws are designed. Feasibility of the proposed scheme is proven in theory. Moreover, two numerical examples are presented, using the energy resource system and Lü＇s system [Physica A 382 （2007） 672] as the nodes of the networks. GPS between two energy resource complex networks with time-varying coupling delay is achieved. This study can widen the application range of the generalized synchronization methods and will be instructive for the demand supply of energy resource in some regions of China.
基金Project supported by the National Natural Science Foundation of China(Grant No.11101191)
文摘In this paper, we give a detailed discussion about the dynamical behaviors of compact solitary waves subjected to the periodic perturbation. By using the phase portrait theory, we find one of the nonsmooth solitary waves of the mKdV equation, namely, a compact solitary wave, to be a weak solution, which can be proved. It is shown that the compact solitary wave easily turns chaotic from the Melnikov theory. We focus on the sufficient conditions by keeping the system stable through selecting a suitable controller. Furthermore, we discuss the chaotic threshold for a perturbed system. Numerical simulations including chaotic thresholds, bifurcation diagrams, the maximum Lyapunov exponents, and phase portraits demonstrate that there exists a special frequency which has a great influence on our system; with the increase of the controller strength, chaos disappears in the perturbed system. But if the controller strength is sufficiently large, the solitary wave vibrates violently.
基金Supported by the National Natural Science Foundation of China under Grant Nos 71073071 and 71273119the Key Program of Social Science Foundation of Jiangsu Provincial Department of Education(No 2010-2-10)the Priority Academic Program Development of Jiangsu Higher Education Institutions,and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No 13KJB120001.
文摘We investigate the synchronization problem of two colored networks via discrete control based on the Lyapunov stability theory.First,intermittent control is adopted to synchronize two edge-colored networks,and the suffi-cient condition connecting the control width,control period and the network topology is established for reaching synchronization.Then,an impulsive controller is designed to ensure two general colored networks in synchroniza-tion,and the relation among the impulsive interval,impulsive gain and the network topology for synchronization is also discovered.Finally,two numerical examples are provided to demonstrate and verify the theoretical results.
基金The project supported by National Natural Science Foundation of China under Grant No. 10071033, the Natural Science Foundation of Jiangsu Province under Grant No. BK2002003, the Project of Technology Innovation Plan for Postgraduate of Jiangsu Province in Year 2006 under Grant No. 72, and the Natural Science Directed Foundation of the Jiangsu Higher Education Institutions under Grant No. 06KJDll0001
文摘Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations.
