奇异态是在非局域耦合条件下耦合相振子或混沌振子系统中形成的同步区域与不同步区域相互隔离的一种斑图。因其在生物学中“半脑睡眠”的现象研究中具有理论指导意义，从而引起了研究人员的广泛关注与兴趣，并成为非线性动力学领域的一个热点问题。本项目主要研究耦合作用的对称性破缺对奇异态特性的影响。以非局域耦合相振子系统为研究对象，采取不同的耦合对称性破缺形式，探究对称性破缺对于奇异态稳定性以及时空斑图的影响，确定“奇异态”存在的参数空间以及耦合强度的临界点。基于OTT-ANTONSEN理论和KURAMOTO-BATTOGTKH自洽方程理论，探讨耦合对称性破缺对奇异态影响的内在机制。由于非对称耦合作用的广泛性，本项目的研究成果具有更加普遍的理论指导意义。

The chimera state is a spatiotemporal pattern in which some of the identical oscillators are coherent and synchronous while others remain incoherent in nonlocally coupled phase oscillators or chaotic oscillators systems. It is attracted the researchers’ attention and interest in the last ten years because chimera states are beneficial to the phenomenon unihemispheric sleep in Biology. And it became a hot issue in the field of nonlinear dynamics. In this project, we study the chimera states by exploring the effects of the asymmetry of the coupling on the chimera states. A phase oscillator model with nonlocal coupling is built. We adopt the several forms of asymmetry of coupling, and study the effects of broken symmetry on the stability and spatiotemporal patterns of chimera states, and determine the critical coupling strength and parameter space for stable chimera states of the coupled system. The intrinsic mechanism of effect of asymmetry on chimera states is researched based on the OTT-ANTONSEN ansatz and KURAMOTO-BATTOGTKH self-consistency equation. The research can provides the general theoretical guidance because the asymmetric coupling is widespread.