Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system

In this paper, a novel four dimensional hyper-chaotic system is coined based on the Chen system, which contains two quadratic terms and five system parameters. The proposed system can generate a hyper-chaotic attractor in wide parameters regions. By using the center manifold theorem and the local bifurcation theory, a pitchfork bifurcation is demonstrated to arise at the zero equilibrium point. Numerical analysis demonstrates that the hyper-chaotic system can generate complex dynamical behaviors, e.g., a direct transition from quasi-periodic behavior to hyper-chaotic behavior. Finally, an electronic circuit is designed to implement the hyper-chaotic system, the experimental results are consist with the numerical simulations, which verifies the existence of the hyper-chaotic attractor. Due to the complex dynamic behaviors, this new hyper-chaotic system is useful in the secure communication.     

Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system

In this paper,a novel four dimensional hyper-chaotic system is coined based on the Chen system,which contains two quadratic terms and five system parameters.The proposed system can generate a hyper-chaotic attractor in wide parameters regions.By using the center manifold theorem and the local bifurcation theory,a pitchfork bifurcation is demonstrated to arise at the zero equilibrium point.Numerical analysis demonstrates that the hyper-chaotic system can generate complex dynamical behaviors,e.g.,a direct transition from quasi-periodic behavior to hyper-chaotic behavior.Finally,an electronic circuit is designed to implement the hyper-chaotic system,the experimental results are consist with the numerical simulations,which verifies the existence of the hyper-chaotic attractor.Due to the complex dynamic behaviors,this new hyper-chaotic system is useful in the secure communication.     

A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system

This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges.Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies.Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.