基于一个新混沌系统的超混沌的产生及其控制

Generating hyperchaos from a new chaotic system and its control

通过在Yassen提出的三阶混沌系统中增加一个状态,从而得到一个新的超混沌系统.研究了新的超混沌系统的基本动力学行为,给出了超混沌系统的吸引子、Lyapunov指数、分维数、分岔图、平衡点以及随着参数的变化新系统的运动轨道在混沌和超混沌之间的演变过程.分别利用非线性双曲函数反馈控制法和线性反馈控制法研究了新系统的超混沌控制问题,讨论了将受控系统的超混沌轨道镇定到不稳定平衡点时的条件.数值模拟进一步验证了所提出方案的有效性.

In this paper, a new hyperchaotic system is presented by introducing an additional state into the third-order chaotic system proposed by Yassen. Some of its basic dynamical properties, such as hyperchaotic attractor, Lyapunov exponent, fractal dimension, plot of bifurcation, equilibrium point and hyperchaotie attractor evolving into chaotic dynamical behaviors with parameter varying are investigated. Various attractors are illustrated by computer simulation. Two different methods, i.e. nonlinear hyperbolic function feedback control and linear feedback control methods are used to control the hyperchaos in the new hyperchaotic system. The conditions suppressing hyperchaos to unstable equilibrium point are discussed. Numerical results show the effectiveness of the control methods.