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中文摘要：
对单向耦合下两个不同的Lorenz系统的广义同步进行了研究,利用辅助系统方法,基于稳定性理论和响应系统的有界性,得到了它们达到广义同步时的充分条件,并根据响应系统的修正系统具有零渐近稳定平衡点、非零渐近稳定平衡点和轨道渐近稳定周期解的情况,将广义同步分为第一类、第二类和第三类;利用Routh-Hurwitz定理,对修正系统平衡点的稳定性进行了分析,给出了单向耦合下两个不同Lorenz系统具有第一类、第二类广义同步的充分条件.数值仿真表明了该方法的有效性与可行性.
英文摘要：
The generalized synchronization （GS） of two different unidirectional coupled Lorenz systems is studied. According to the method of auxiliary-system, by using the theories of stability and the boundary of the responsed system, a sufficient criterion is rigorously proven. Furthermore, based on the modified system approach, GS is classified into three types, the first type,the second type and the th ird type of GS when the modified system has an asymptotically stable equilibrium of zero solution, asymptotically stable equilibrium of non-zero solution, asymptotically stable limit cycles, respectively. Moreover, using the Routh-Hurwitz theorem to analyze the stability of equilibrium of the modified system, the existence of the first type and the second type of GS are strictly theoretically proved. Numerical simulations show the effectiveness of the method.
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