Manoranjani M, Gopal R, Senthilkumar D V, Chandrasekar V K, Lakshmanan M
Department of Physics, Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, India.
School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016, India.
Phys Rev E. 2022 Mar;105(3-1):034307. doi: 10.1103/PhysRevE.105.034307.
We investigate the phase diagram of the Sakaguchi-Kuramoto model with a higher-order interaction along with the traditional pairwise interaction. We also introduce asymmetry parameters in both the interaction terms and investigate the collective dynamics and their transitions in the phase diagrams under both unimodal and bimodal frequency distributions. We deduce the evolution equations for the macroscopic order parameters and eventually derive pitchfork and Hopf bifurcation curves. Transition from the incoherent state to standing wave pattern is observed in the presence of the unimodal frequency distribution. In contrast, a rich variety of dynamical states such as the incoherent state, partially synchronized state-I, partially synchronized state-II, and standing wave patterns and transitions among them are observed in the phase diagram via various bifurcation scenarios, including saddle-node and homoclinic bifurcations, in the presence of bimodal frequency distribution. Higher-order coupling enhances the spread of the bistable regions in the phase diagrams and also leads to the manifestation of bistability between incoherent and partially synchronized states even with unimodal frequency distribution, which is otherwise not observed with the pairwise coupling. Further, the asymmetry parameters facilitate the onset of several bistable and multistable regions in the phase diagrams. Very large values of the asymmetry parameters allow the phase diagrams to admit only the monostable dynamical states.
我们研究了具有高阶相互作用以及传统成对相互作用的坂口-仓本模型的相图。我们还在相互作用项中引入了不对称参数，并研究了在单峰和双峰频率分布下相图中的集体动力学及其转变。我们推导了宏观序参量的演化方程，并最终得出叉形分岔曲线和霍普夫分岔曲线。在单峰频率分布的情况下，观察到从不相干态到驻波模式的转变。相比之下，在双峰频率分布的情况下，通过各种分岔情形，包括鞍结分岔和同宿分岔，在相图中观察到了丰富多样的动力学状态，如非相干态、部分同步态-I、部分同步态-II和驻波模式以及它们之间的转变。高阶耦合增强了相图中双稳区域的范围，并且即使在单峰频率分布下也会导致非相干态和部分同步态之间双稳性的表现，而在成对耦合情况下则不会观察到这种情况。此外，不对称参数促进了相图中几个双稳和多稳区域的出现。非常大的不对称参数值使得相图仅允许单稳动力学状态。
