Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India.
School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695016, India.
Phys Rev E. 2018 Mar;97(3-1):032207. doi: 10.1103/PhysRevE.97.032207.
We investigate the effect of repulsive coupling together with an attractive coupling in a network of nonlocally coupled oscillators. To understand the complex interaction between these two couplings we introduce a control parameter in the repulsive coupling which plays a crucial role in inducing distinct complex collective patterns. In particular, we show the emergence of various cluster chimera death states through a dynamically distinct transition route, namely the oscillatory cluster state and coherent oscillation death state as a function of the repulsive coupling in the presence of the attractive coupling. In the oscillatory cluster state, the oscillators in the network are grouped into two distinct dynamical states of homogeneous and inhomogeneous oscillatory states. Further, the network of coupled oscillators follow the same transition route in the entire coupling range. Depending upon distinct coupling ranges, the system displays different number of clusters in the death state and oscillatory state. We also observe that the number of coherent domains in the oscillatory cluster state exponentially decreases with increase in coupling range and obeys a power-law decay. Additionally, we show analytical stability for observed solitary state, synchronized state, and incoherent oscillation death state.
我们研究了排斥耦合与非局部耦合振子网络中吸引耦合的共同作用。为了理解这两种耦合之间的复杂相互作用，我们在排斥耦合中引入了一个控制参数，它在诱导不同的复杂集体模式方面起着至关重要的作用。特别是，我们通过动态上不同的过渡途径展示了各种簇奇异死亡状态的出现，即作为吸引耦合存在时排斥耦合的振荡簇状态和相干振荡死亡状态。在振荡簇状态中，网络中的振荡器被分为同质和非同质振荡状态的两种不同动力学状态。此外，耦合振荡器网络在整个耦合范围内遵循相同的过渡途径。根据不同的耦合范围，系统在死亡状态和振荡状态下显示出不同数量的簇。我们还观察到，振荡簇状态中的相干域数量随耦合范围的增加呈指数减少，并服从幂律衰减。此外，我们还展示了观察到的孤立态、同步态和非相干振荡死亡态的分析稳定性。
