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Hexagonal standing-wave patterns in periodically forced reaction-diffusion systems

机译:周期性强迫反应扩散系统中的六角形驻波图

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The periodically forced spatially extended Brusselator is investigated in the oscillating regime. The temporal response and pattern formation within the 2:1 frequency-locking band where the system oscillates at one half of the forcing frequency are examined. An hexagonal standing-wave pattern and other resonant patterns are observed. The detailed phase diagram of resonance structure in the forcing frequency and forcing amplitude parameter space is calculated. The transitions between the resonant standing-wave patterns are of hysteresis when control parameters are varied, and the presence of multiplicity is demonstrated. Analysis in the framework of amplitude equation reveals that the spatial patterns of the standing waves come out as a result of Turing bifurcation in the amplitude equation.
机译:在振动状态下研究了周期性强制空间扩展的Brusselator。检查系统在强迫频率的一半处振荡的2:1锁频带内的时间响应和模式形成。观察到六边形驻波图案和其他共振图案。计算了在强迫频率和强迫幅度参数空间中共振结构的详细相图。当控制参数变化时,谐振驻波模式之间的过渡具有滞后性,并且证明了多重性的存在。在幅度方程框架内的分析表明,驻波的空间模式是幅度方程中图灵分叉的结果。

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