In this paper,a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further,to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied eith...In this paper,a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further,to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nu-merically,such as Poincaré map,Lyapunov exponents and Lyapunov dimension. Based on this flow,a new almost-Hamilton chaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.展开更多
To improve the performance of chaotic secure communication,three simplified chaotic systems with one variable parameter were investigated.Basic properties were analyzed including symmetry,dissipation and topological s...To improve the performance of chaotic secure communication,three simplified chaotic systems with one variable parameter were investigated.Basic properties were analyzed including symmetry,dissipation and topological structure.Complex dynamical behaviors of the systems including chaos and periodic orbits were verified by numerical simulations,Lyapunov exponents and bifurcation diagrams.Interestingly,the three systems were integrated in a common circuit,and their dynamical behaviors were easily observed by adjusting regulable resistors R28,R14 and R17,respectively,and the relations between the variable resistor and the system parameter were deduced.The circuit experiment results agree well with the simulation results.Finally,a secure communication scheme based on chaos shift keying(CSK) was presented,which lays an experiment foundation for chaotic digital secure communication.展开更多
To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coup...To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.展开更多
Routes to chaos in power systems are studied. Using a three-bus simple system, three routes that can lead power system to chaos are presented, illustrated and discussed. They are cascading period doubling bifurcation,...Routes to chaos in power systems are studied. Using a three-bus simple system, three routes that can lead power system to chaos are presented, illustrated and discussed. They are cascading period doubling bifurcation, torus bifurcation and route directly initiated by a large disturbance. Period doubling bifurcation is caused by a real Floquet multiplier going out of the unit circle from point (-1,0), while torus bifurcation is caused by a couple of conjugated Floquet multipliers going out of the unit circle with a non-zero imaginary part in the complex plane. Cascading period doubling bifurcation and torus bifurcation are two typical routes to chaos in dynamic systems, which have been investigated in the previous studies. The last route, i.e. directly initiated by a large disturbance, is reported and studied. This phenomenon reveals that chaos is caused by external disturbances in power systems.展开更多
A new control law is proposed to asymptotically stabilize the chaotic neuron system based on LaSalleinvariant principle.The control technique does not require analytical knowledge of the system dynamics and operateswi...A new control law is proposed to asymptotically stabilize the chaotic neuron system based on LaSalleinvariant principle.The control technique does not require analytical knowledge of the system dynamics and operateswithout an explicit knowledge of the desired steady-state position.The well-known modified Hodgkin-Huxley (MHH)and Hindmarsh-Rose (HR) model neurons are taken as examples to verify the implementation of our method.Simulationresults show the proposed control law is effective.The outcome of this study is significant since it is helpful to understandthe learning process of a human brain towards the information processing,memory and abnormal discharge of the brainneurons.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 50475109)the Natural Science Foundation of Gansu Province (No. 3ZS-042-B25-049), China
文摘In this paper,a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further,to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nu-merically,such as Poincaré map,Lyapunov exponents and Lyapunov dimension. Based on this flow,a new almost-Hamilton chaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.
基金Projects(611061006,61073187) supported by the National Nature Science Foundation of China
文摘To improve the performance of chaotic secure communication,three simplified chaotic systems with one variable parameter were investigated.Basic properties were analyzed including symmetry,dissipation and topological structure.Complex dynamical behaviors of the systems including chaos and periodic orbits were verified by numerical simulations,Lyapunov exponents and bifurcation diagrams.Interestingly,the three systems were integrated in a common circuit,and their dynamical behaviors were easily observed by adjusting regulable resistors R28,R14 and R17,respectively,and the relations between the variable resistor and the system parameter were deduced.The circuit experiment results agree well with the simulation results.Finally,a secure communication scheme based on chaos shift keying(CSK) was presented,which lays an experiment foundation for chaotic digital secure communication.
基金Projects(61073187,61161006) supported by the National Nature Science Foundation of ChinaProject supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry,China
文摘To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.
基金Supported by the Foundation for the Author of National Excellent Doctoral Dissertation(No.200439)Key Project of Chinese Ministryof Education (No.105047)+2 种基金Program for New Century Excellent Talents in University,Fok Ying Tung Education Foundation(No.104019)Innovation Fund of Tianjin Municipal(No.06TXTJJC13700),Natural Science Foundation of China(No.50595413) theSpecial Fund of the National Fundamental Research (2004CB217904)of China.
文摘Routes to chaos in power systems are studied. Using a three-bus simple system, three routes that can lead power system to chaos are presented, illustrated and discussed. They are cascading period doubling bifurcation, torus bifurcation and route directly initiated by a large disturbance. Period doubling bifurcation is caused by a real Floquet multiplier going out of the unit circle from point (-1,0), while torus bifurcation is caused by a couple of conjugated Floquet multipliers going out of the unit circle with a non-zero imaginary part in the complex plane. Cascading period doubling bifurcation and torus bifurcation are two typical routes to chaos in dynamic systems, which have been investigated in the previous studies. The last route, i.e. directly initiated by a large disturbance, is reported and studied. This phenomenon reveals that chaos is caused by external disturbances in power systems.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10862001 and 10947011the Construction of Key Laboratories in Universities of Guangxi under Grant No. 200912
文摘A new control law is proposed to asymptotically stabilize the chaotic neuron system based on LaSalleinvariant principle.The control technique does not require analytical knowledge of the system dynamics and operateswithout an explicit knowledge of the desired steady-state position.The well-known modified Hodgkin-Huxley (MHH)and Hindmarsh-Rose (HR) model neurons are taken as examples to verify the implementation of our method.Simulationresults show the proposed control law is effective.The outcome of this study is significant since it is helpful to understandthe learning process of a human brain towards the information processing,memory and abnormal discharge of the brainneurons.
