时滞自同步控制振荡反应扩散系统的时空混沌
Controlling spatiotemporal chaos in oscillatory reaction-diffusion systems by time-delay autosynchronization
摘要：
在超临界Hopf分岔附近的空间扩展振荡介质中，扩散诱导的湍流可以通过应用全局时滞自同步来控制。我们考虑了Benjamin-Feir不稳定区域中的复Ginzburg-Landau方程，并解析地研究了依赖于反馈参数的一致振荡的稳定性。我们表明，在这种类型的系统的非侵入性稳定的均匀振荡是不可能的。导出了反馈参数所覆盖的平面内的同步图。数值模拟证实了分析结果，并给出了额外的信息接近完全同步的系统的时空动力学。
英文摘要：
Diffusion-induced turbulence in spatially extended oscillatory media near a supercritical Hopf bifurcation can be controlled by applying global time-delay autosynchronization. We consider the complex Ginzburg-Landau equation in the Benjamin-Feir unstable regime and analytically investigate the stability of uniform oscillations depending on the feedback parameters. We show that a noninvasive stabilization of uniform oscillations is not possible in this type of systems. The synchronization diagram in the plane spanned by the feedback parameters is derived. Numerical simulations confirm the analytical results and give additional information on the spatiotemporal dynamics of the system close to complete synchronization.
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