Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK.
Philos Trans A Math Phys Eng Sci. 2013 Aug 19;371(1999):20120466. doi: 10.1098/rsta.2012.0466. Print 2013 Sep 28.
This paper studies the effects of distributed-delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, the conditions for amplitude death are obtained in terms of average frequency, frequency detuning and the parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insights into the dynamics inside amplitude death regions, the eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated, using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions.
本文研究了分布式时滞耦合对非一致耦合 Stuart-Landau 振荡器系统动力学的影响。对于均匀和伽马延迟分布核，通过平均频率、频率失谐以及耦合参数（包括耦合强度和相位），以及平均延迟时间和延迟分布的宽度，得到了振幅死亡的条件。为了更深入地了解振幅死亡区域内的动力学，通过数值计算得到了相应特征方程的特征值。还使用幅度和相位表示法研究了系统的振荡动力学。确定了相位锁定解的各种分支，并分析了不同类型延迟分布的稳定性。
