“奇异态”是同步区域与不同步区域相互隔离的一种斑图，在近十年间引起了研究人员的广泛关注与兴趣，是非线性动力学领域的一个热点问题。先前大部分的“奇异态”的研究都集中在规则格子中。本项目主要是通过复杂网络的拓扑结构对“奇异态”的影响来研究复杂网络上“奇异态”的生成机制与稳定性。以非局域耦合相振子为研究对象，应用OTT-ANTONSEN理论和KURAMOTO-BATTOGTKH自洽方程来确定“奇异态”存在的参数空间以及耦合强度的临界点，进而寻求在复杂网络上“奇异态”形成的内在机制与规律。本课题的研究结果对生物学上“半脑睡眠”现象的研究具有参考作用。

The chimera state is a spatiotemporal pattern in which some of the identical oscillators are coherent and synchronous while others remain incoherent. It is attracted the researchers’ attention and interest in the last ten years and is a hot issue in the field of nonlinear dynamics. Previous studies on the chimera states most focused on the regular lattices. In this project, we study the emerging and stability of chimera states in complex networks by exploring the effects of the topology of complex networks on the chimera states. A phase oscillator model with nonlocal coupling is built. The critical coupling strength and parameter space for stable chimera states of the coupled system are determined based on the OTT-ANTONSEN ansatz and KURAMOTO-BATTOGTKH self-consistency equation. Moreover, we expect to uncover the internal mechanisms and universal laws of the chimera states in complex networks. The research may be beneficial to the phenomenon unihemispheric sleep in Biology.