基于Lorenz系统的强迫Lorenz混沌系统的动力学研究

Dynamical behavior for the forced Lorenz system based on the Lorenz map and simulation

通过给出了强迫Lorenz混沌系统的动力系统模型,借助一簇广义正定、径向无界的Lyapunov函数和最优化理论研究了混沌系统的正半轨线的有界性,得到了正半轨线界估计的表达式,数值模拟表明了方案的可行性.

The boundedness of a chaotic system is important in chaos control, synchronization and other applications. The boundedness of the forced Lorenz system is investigated via constructing a family of Lyapunov functions and optimation theory. The globally exponentially attractive set and positive invariant set are obtained for this system. Furthermore, we can conclude that the rate of the trajectories of the system going from the exterior of the setΩλ to the interior of the set Ωλ is an exponential rate. The estimate of the trajectories rate is also obtained. Numerical simulations are presented to show the effectiveness of the proposed scheme.