D'Huys Otti, Jüngling Thomas, Kinzel Wolfgang
Institute of Theoretical Physics, University of Würzburg, 97074 Würzburg, Germany.
Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):032918. doi: 10.1103/PhysRevE.90.032918. Epub 2014 Sep 19.
A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators we reduce the delay system to a nondelayed Langevin equation, which allows us to analytically compute the distribution of frequencies and their corresponding residence times. The number of stable periodic orbits scales with the roundtrip delay time and coupling strength, but the noisy system visits only a fraction of the orbits, which scales with the square root of the delay time and is independent of the coupling strength. In contrast, the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators, and only weakly dependent on the coupling delay. Finally we investigate the effect of a detuning between the oscillators. We demonstrate the generality of our results with delay-coupled FitzHugh-Nagumo oscillators.
已知延迟会在周期系统中引发多稳态。在噪声影响下，耦合振子可以在具有不同频率和不同振荡模式的共存轨道之间切换。对于耦合相位振子，我们将延迟系统简化为一个无延迟的朗之万方程，这使我们能够解析计算频率分布及其相应的驻留时间。稳定周期轨道的数量与往返延迟时间和耦合强度有关，但有噪声的系统仅访问轨道的一部分，这部分轨道数量与延迟时间的平方根有关，且与耦合强度无关。相比之下，在不同轨道中的驻留时间主要由耦合强度和振子数量决定，仅微弱地依赖于耦合延迟。最后，我们研究了振子之间失谐的影响。我们用延迟耦合的菲茨休 - 纳古莫振子证明了我们结果的普遍性。
