反应扩散系统复杂振荡模式的相位和振幅描述
Phase and amplitude description of complex oscillatory patterns in reaction-diffusion systems
摘要：
自发节律振荡广泛存在于各种实际系统中。特别是，生物节律，通常通过许多自振荡细胞的同步产生，通常在生命系统中发挥重要的功能作用。分析振动系统同步动力学的标准理论方法之一是弱扰动极限环振子的相位约化，它允许我们将表现稳定极限环振动的非线性动力学模型简化为简单的一维相位方程。最近，经典的相位缩减方法已被推广到无限维的振荡系统，如空间扩展系统和时滞系统，也包括振幅自由度表示的系统状态从未扰动的极限环的偏差。在这一章中，我们讨论了具有稳定振荡模式的空间扩展反应扩散系统的相位振幅缩减方法。作为应用，我们分析了一个反应扩散系统的夹带表现出极限环振荡的优化周期强迫和额外的反馈镇定。
英文摘要：
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in living systems. One of the standard theoretical methods for analyzing synchronization dynamics of oscillatory systems is the phase reduction for weakly perturbed limit-cycle oscillators, which allows us to simplify nonlinear dynamical models exhibiting stable limit-cycle oscillations to a simple one-dimensional phase equation. Recently, the classical phase reduction method has been generalized to infinite-dimensional oscillatory systems such as spatially extended systems and time-delayed systems, and also to include amplitude degrees of freedom representing deviations of the system state from the unperturbed limit cycle. In this chapter, we discuss the method of phase-amplitude reduction for spatially extended reaction-diffusion systems exhibiting stable oscillatory patterns. As an application, we analyze entrainment of a reaction-diffusion system exhibiting limit-cycle oscillations by an optimized periodic forcing and additional feedback stabilization.
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