College of Chemical Engineering, China University of Mining and Technology, Xuzhou, China.
Chaos. 2009 Sep;19(3):033134. doi: 10.1063/1.3224031.
The periodically forced Brusselator model displays temporal mixed-mode and quasiperiodic oscillations, period doubling, and chaos. We explore the behavior of such media as reaction-diffusion systems for investigating spiral instabilities. Besides near-core breakup and far-field breakup resulting from unstable modes in the radial direction or Doppler-induced instability (destabilization of the core's location), the observed complex phenomena include backfiring, spiral regeneration, and amplitude modulation from line defects. Amplitude modulation of spirals can evolve to chambered spirals resembling those found in nature, such as pine cones and sunflowers. When the forcing amplitude is increased, the spiral-tip meander evolves from simple rotation to complex petals, corresponding to transformation of the local dynamics from simple oscillations to mixed-mode, period-2, and quasiperiodic oscillations. The number of petals is related to the complexity of the mixed-mode oscillations. Spiral turbulence, standing waves, and homogeneous synchronization permeate the entire system when the forcing amplitude is further increased.
周期强制布鲁塞尔ator 模型表现出时间混合模式和准周期振荡、倍周期和混沌。我们探索了作为反应扩散系统的介质的行为，以研究螺旋不稳定性。除了由于径向不稳定模式或多普勒诱导不稳定性（核心位置失稳）导致的近核破裂和远场破裂之外，观察到的复杂现象还包括反向点火、螺旋再生和线缺陷引起的振幅调制。螺旋的振幅调制可以演变成类似于自然界中发现的腔室螺旋，如松果和向日葵。当强迫振幅增加时，螺旋尖端蜿蜒从简单旋转演变为复杂的花瓣，对应于局部动力学从简单振荡到混合模式、倍周期和准周期振荡的转变。花瓣的数量与混合模式振荡的复杂性有关。当强迫振幅进一步增加时，螺旋湍流、驻波和均匀同步渗透整个系统。
