Department of Physics, East China Normal University, Shanghai 200062, People's Republic of China.
School of Data Science, Tongren University, Tongren 554300, People's Republic of China.
Phys Rev E. 2017 Nov;96(5-1):052209. doi: 10.1103/PhysRevE.96.052209. Epub 2017 Nov 14.
Chimera state has been well studied recently, but little attention has been paid to its transition to synchronization. We study this topic here by considering two groups of adaptively coupled Kuramoto oscillators. By searching the final states of different initial conditions, we find that the system can easily show a chimera state with robustness to initial conditions, in contrast to the sensitive dependence of chimera state on initial conditions in previous studies. Further, we show that, in the case of symmetric couplings, the behaviors of the two groups are always complementary to each other, i.e., robustness of chimera state, except a small basin of synchronization. Interestingly, we reveal that the basin of synchronization will be significantly increased when either the coupling of inner groups or that of intergroups are asymmetric. This transition from the attractor of chimera state to the attractor of synchronization is closely related to both the phase delay and the asymmetric degree of coupling strengths, resulting in a diversity of attractor's patterns. A theory based on the Ott-Antonsen ansatz is given to explain the numerical simulations. This finding may be meaningful for the control of competition between two attractors in biological systems, such as the cardiac rhythm and ventricular fibrillation, etc.
最近人们对嵌合体状态进行了深入研究，但对其向同步的转变关注较少。我们通过考虑两组自适应耦合的 Kuramoto 振子来研究这个问题。通过搜索不同初始条件的最终状态，我们发现系统可以很容易地表现出对初始条件具有鲁棒性的嵌合体状态，这与之前研究中嵌合体状态对初始条件的敏感依赖性形成了对比。此外，我们表明，在对称耦合的情况下，两组的行为总是互补的，即除了小范围的同步外，嵌合体状态具有鲁棒性。有趣的是，我们揭示了当内群或外群的耦合不对称时，同步的范围将会显著增加。这种从嵌合体状态的吸引子到同步的吸引子的转变与相位延迟和耦合强度的不对称程度密切相关，导致吸引子模式的多样性。基于 Ott-Antonsen 假设的理论被用来解释数值模拟。这一发现可能对控制生物系统中两个吸引子之间的竞争具有重要意义，如心脏节律和心室颤动等。
