This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fra...This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.展开更多
The eigenvalue space of the canonical four-dimensional Chua＇s circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parame...The eigenvalue space of the canonical four-dimensional Chua＇s circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parameters and the eigenvalues of the system are established, and therefore all the circuit parameters can be determined explicitly by any given set of eigenvalues. Then, the eigenvalue space of the circuit is investigated in two cases by the nonlinear elements used. According to the types of the eigenvalues, some novel hyperchaotic attractors are presented. Further, the dynamic behaviours of the circuit are studied by the bifurcation diagrams and the Lyapunov spectra of the eigenvalues.展开更多
Based on the three-dimensional Liu system with a nonlinear term of square, this paper appends a state variable to the system, and further adds a driving signal of the sine signal to construct a novel 4-demensional non...Based on the three-dimensional Liu system with a nonlinear term of square, this paper appends a state variable to the system, and further adds a driving signal of the sine signal to construct a novel 4-demensional nonautonomous hyperchaotic Liu system. The appended variable is formed by the product of the nonlinear quadratic term of the original state variables and the driving signal. Through adjusting the frequency of the driving signal, the system can be controlled to show some different dynamic behaviors. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the novel systems are analyzed. Furthermore, the corresponding hardware circuits are implemented. Both the experimental results and the simulation results confirm that the method is feasible. The method, which adjusts the frequency of the input sine signal to control the system to show different dynamic behaviors, can make the dynamic property of the system become more complex, but easier to be controlled accurately as well.展开更多
In this manuscript, Local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional quadratic autonomous system are studied both analytically and numerically. Determining conditions of equil...In this manuscript, Local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional quadratic autonomous system are studied both analytically and numerically. Determining conditions of equilibrium points on different parameters are derived. Next, the stability conditions are investigated by using Routh-Hurwitz criterion and bifurcation conditions are investigated by using Hopf bifurcation theory, respectively. It is found that Hopf bifurcation on the initial point is supercritical in this four-dimensional autonomous system. The theoretical results are verified by numerical simulation. Besides, the new four-dimensional autonomous system under the parametric conditions of hyperchaos is studied in detail. It is also found that the system can enter hyperchaos, first through Hopf bifurcation and then through periodic bifurcation.展开更多
文摘This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50877007)
文摘The eigenvalue space of the canonical four-dimensional Chua＇s circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parameters and the eigenvalues of the system are established, and therefore all the circuit parameters can be determined explicitly by any given set of eigenvalues. Then, the eigenvalue space of the circuit is investigated in two cases by the nonlinear elements used. According to the types of the eigenvalues, some novel hyperchaotic attractors are presented. Further, the dynamic behaviours of the circuit are studied by the bifurcation diagrams and the Lyapunov spectra of the eigenvalues.
基金supported by the National Natural Science Foundation of China (Grant No 60572089)the Natural Science Foundation of Chongqing (Grant No CSTC,2008BB2087)
文摘Based on the three-dimensional Liu system with a nonlinear term of square, this paper appends a state variable to the system, and further adds a driving signal of the sine signal to construct a novel 4-demensional nonautonomous hyperchaotic Liu system. The appended variable is formed by the product of the nonlinear quadratic term of the original state variables and the driving signal. Through adjusting the frequency of the driving signal, the system can be controlled to show some different dynamic behaviors. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the novel systems are analyzed. Furthermore, the corresponding hardware circuits are implemented. Both the experimental results and the simulation results confirm that the method is feasible. The method, which adjusts the frequency of the input sine signal to control the system to show different dynamic behaviors, can make the dynamic property of the system become more complex, but easier to be controlled accurately as well.
文摘In this manuscript, Local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional quadratic autonomous system are studied both analytically and numerically. Determining conditions of equilibrium points on different parameters are derived. Next, the stability conditions are investigated by using Routh-Hurwitz criterion and bifurcation conditions are investigated by using Hopf bifurcation theory, respectively. It is found that Hopf bifurcation on the initial point is supercritical in this four-dimensional autonomous system. The theoretical results are verified by numerical simulation. Besides, the new four-dimensional autonomous system under the parametric conditions of hyperchaos is studied in detail. It is also found that the system can enter hyperchaos, first through Hopf bifurcation and then through periodic bifurcation.
