Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.
Chaos. 2011 Jun;21(2):023122. doi: 10.1063/1.3596697.
We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from other oscillators in its neighborhood. Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)] and adopting a strategy similar to that employed in the recent work of Laing [Physica D 238, 1569 (2009)], we reduce the microscopic dynamics of these systems to a macroscopic partial-differential-equation description. Using this macroscopic formulation, we numerically find that finite oscillator response time leads to interesting spatiotemporal dynamical behaviors including propagating fronts, spots, target patterns, chimerae, spiral waves, etc., and we study interactions and evolutionary behaviors of these spatiotemporal patterns.
我们考虑了许多空间分布的相振荡器系统，这些系统与它们的邻居相互作用。每个振荡器都允许有不同的自然频率，以及对其邻居中其他振荡器接收到的信号的不同响应时间。我们使用 Ott 和 Antonsen [Chaos 18, 037113 (2008)] 的假设，并采用与最近 Laing [Physica D 238, 1569 (2009)] 的工作中类似的策略，将这些系统的微观动力学简化为宏观的偏微分方程描述。使用这个宏观公式，我们通过数值计算发现，有限的振荡器响应时间会导致有趣的时空动力学行为，包括传播前沿、斑点、目标图案、嵌合体、螺旋波等，我们研究了这些时空模式的相互作用和演化行为。
