Thamizharasan S, Chandrasekar V K, Senthilvelan M, Senthilkumar D V
Department of Nonlinear Dynamics, School of Physics, <a href="https://ror.org/02w7vnb60">Bharathidasan University</a>, Tiruchirappalli 620 024, Tamil Nadu, India.
Centre for Nonlinear Science and Engineering, Department of Physics, School of Electrical and Electronics Engineering, <a href="https://ror.org/032jk8892">SASTRA Deemed University</a>, Thanjavur 613 401, Tamil Nadu, India.
Phys Rev E. 2024 Sep;110(3-1):034217. doi: 10.1103/PhysRevE.110.034217.
We consider an adaptive network of identical phase oscillators with the symmetric adaptation rule for the evolution of the connection weights under the influence of an external force. We show that the adaptive network exhibits a plethora of self-organizing dynamical states such as the two-cluster state, multiantipodal clusters, splay cluster, splay chimera, forced entrained state, chimera state, bump state, coherent, and incoherent states in the two-parameter phase diagrams. The intriguing structures of the frequency clusters and instantaneous phases of the oscillators characterize the distinct self-organized synchronized and partial synchronized states. The hierarchical organization of the frequency clusters, resulting in strongly coupled subnetworks, is also evident from the dynamics of the coupling weights, where the frequency clusters are either very weakly coupled or even completely decoupled from each other. Additionally, we also deduce the stability condition for the forced entrained state.
我们考虑一个由相同相位振荡器组成的自适应网络，在外部力的影响下，连接权重的演化遵循对称自适应规则。我们表明，在双参数相图中，自适应网络展现出大量自组织动态状态，如双簇状态、多对映体簇、展开簇、展开嵌合体、强迫同步状态、嵌合体状态、凸起状态、相干和非相干状态。振荡器的频率簇和瞬时相位的有趣结构表征了不同的自组织同步和部分同步状态。频率簇的层次组织导致了强耦合子网，这从耦合权重的动态中也很明显，其中频率簇要么彼此耦合非常弱，要么甚至完全解耦。此外，我们还推导了强迫同步状态的稳定性条件。
