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中文摘要：
引入外激和参激两种不同形式的谐和共振激励,探讨了一类约瑟夫森结（Josephson junction）系统的混沌控制问题.利用Melnikov方法研究了异宿混沌的生成和抑制,得到了在一定的控制激励振幅范围内,能确保异宿混沌被控制住,而且推导出控制激励与系统的激励两者之间的相位差和两者频率之间的共振阶数应满足的关系式.从定性的角度说明相位差在异宿混沌的控制中确实有着至关重要的影响,而且,数值方法的研究表明可通过调节相位来控制非自治系统中的稳态混沌.通过分析、比较外激和参激两种不同的共振激励对约瑟夫森结系统的异宿混沌的控制效果,得到对于较小的共振频率,宜采用参激激励,而对于较大的共振频率,宜采用外激激励.
英文摘要：
In the present paper, the control of chaos in the Josephson junction with two different kinds of resonant harmonic excitations, namely the additive and parametric excitations, are investigated in detail. With the Melnikov method, we have obtained the regions of excitation amplitude in which heteroclinic chaos may be generated or suppressed. Meanwhile, for suppressing the heteroclinic chaos, we have determined the prereguisite relationships between parameters of the system excitation and the control excitation. The analytical results show that phase difference between the two excitations has important effect. Moreover, numerical methods show that the phase control method is feasible not only for controlling heteroclinic chaos, but also for controlling other types of chaos in nonautonomous systems. Comparing the effect of an additive harmonious excitation with that of a parametric one, we find the former one is more effective at the small resonant frequencies, while the latter one is more effective at the large ones.
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