Kim Ryong-Son, Choe Chol-Ung
Research Group for Nonlinear Dynamics, Department of Physics, University of Science, Unjong-District, Pyongyang, Democratic People's Republic of Korea.
Chaos. 2019 Feb;29(2):023101. doi: 10.1063/1.5079472.
We consider a network of coupled oscillators embedded in the surface of a sphere with nonlocal coupling strength and heterogeneous phase lags. A nonlocal coupling scheme with heterogeneous phase lags that allows the system to be solved analytically is suggested and the main effects of heterogeneity in the phase lags on the existence and stability of steady states are analyzed. We explore the stability of solutions along the Ott-Antonsen invariant manifold and present a complete bifurcation diagram for stationary patterns including the coherent, incoherent, and modulated drift states as well as chimera state. The stability analysis shows that a continuum of uniform drift states and the modulated drift state could become stable only due to the heterogeneity of the phase lags and that the chimera state is bifurcated from the modulated drift state. Our theoretical results are verified by using the direct numerical simulations of the model system.
我们考虑一个嵌入在具有非局部耦合强度和异质相位滞后的球体表面的耦合振子网络。提出了一种具有异质相位滞后的非局部耦合方案，该方案允许对系统进行解析求解，并分析了相位滞后的异质性对稳态的存在性和稳定性的主要影响。我们研究了沿Ott-Antonsen不变流形的解的稳定性，并给出了包括相干、非相干和调制漂移态以及奇异态在内的静止模式的完整分岔图。稳定性分析表明，均匀漂移态和调制漂移态的连续统仅由于相位滞后的异质性而变得稳定，并且奇异态从调制漂移态分岔出来。我们的理论结果通过对模型系统的直接数值模拟得到了验证。
