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应用常数项控制方法对Lü系统的对称性和耗散性进行了分析,指出了存在的吸引子情况,并对控制常数m在不同情况下的平衡点以及各个平衡点处的系统稳定性进行了分析。当控制常数|m|>48时,系统能收敛到一个平衡点;当0<|m|<48时,系统不能收敛到平衡点,而是控制到对称的极限环或处于混沌状态。在Matlab数值仿真结果中验证了这一过程,它揭示了混沌产生的机制。
The symmetry and dissipative properties of Lü system are analyzed by using the constant term control method. The existence of the attractive attractor is pointed out. The equilibrium point of the control constant m in different situations and the stability of the system at each equilibrium point analysis. When the control | m |> 48, the system can converge to an equilibrium point; when 0 <| m | <48, the system can not converge to the equilibrium point, but control to the symmetric limit cycle or in chaos. This process is verified in Matlab numerical simulation results, which reveals the mechanism of chaos generation.