【摘要】 在耦合振子系统中，表现为具有振幅空间相关性的振子与空间非相关性的振子共存的幅度奇异态与动物半脑睡眠的内在机制密切相关，因其具有初值敏感性和存活时间较短的特点而常被认为是走向系统同步时的过渡态.该文通过在耦合系统中引入吸引与排斥耦合作用，耦合神经元振子系统会随着吸引耦合作用强度的增加从相位奇异态走向稳定的幅度奇异态和死亡奇异态.幅度奇异态的团数随耦合作用半径增加而按幂律关系减小.通过对2个耦合振子分析，发现稳定幅度奇异态的形成机制源于耦合引起的霍普夫分岔而产生振荡中心为一正一负的2个小振幅振荡与原有大振幅振荡的竞争.随着耦合作用的进一步增加，这2个一正一负的小振幅振荡均走向振荡死亡.当耦合半径增加时，它们的竞争最终形成死亡奇异态.更多还原

【Abstract】 The amplitude chimera, characterized by the coexistence of spatially correlated oscillators and spatially noncoherent oscillators in coupled oscillators, is closely related to the internal mechanism of animal unihemispheric sleep.Because of its characteristics of the sensitivity to the initial values and the short survival time, it is often regarded as a transition state towards system synchronization.By introducing attractive and repulsive coupling, the coupled neuron oscillators may transit from phase chimera state to stable amplitude chimera state and death chimera state with the increment of the attractive coupling intensity.The cluster number of the amplitude chimera states decreases with the increment of the coupling radius with a relation of power law.With the analysis of the model of two coupled oscillators, it is found that the stable amplitude chimera state is formed by the competition between a coupled of small amplitude oscillations with positive and negative rotation center generated by the Hopf bifurcation and the original large amplitude oscillation.With the further increment of the coupling strength, the small amplitude oscillation moves towards the oscillation death with positive value and negative values which may form the amplitude death chimera state with the competition between them as the coupling radius increases.更多还原