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Bifurcations to travelling planar spots in a three-component FitzHugh-Nagumo system

机译:三分量FitzHugh-Nagumo系统中行进的平面点的分支

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摘要

In this article, we analyse bifurcations from stationary stable spots to travelling spots in a planar three-component FitzHugh-Nagumo system that was proposed previously as a phenomenological model of gas-discharge systems. By combining formal analyses, center-manifold reductions, and detailed numerical continuation studies, we show that, in the parameter regime under consideration, the stationary spot destabilizes either through its zeroth Fourier mode in a Hopf bifurcation or through its first Fourier mode in a pitchfork or drift bifurcation, whilst the remaining Fourier modes appear to create only secondary bifurcations. Pitchfork bifurcations result in travelling spots, and we derive criteria for the criticality of these bifurcations. Our main finding is that supercritical drift bifurcations, leading to stable travelling spots, arise in this model, which does not seem possible for its two-component version.
机译:在本文中,我们分析了平面三组分FitzHugh-Nagumo系统中从固定稳定点到行进点的分叉,该平面三点组成的FitzHugh-Nagumo系统以前作为气体排放系统的现象学模型提出。通过形式分析,中心流形减少和详细的数值连续性研究的结合,我们表明,在所考虑的参数体系中,固定点通过霍夫夫分叉的零傅立叶模式或干草叉的第一傅立叶模式不稳定或漂移分叉,而其余的傅立叶模式似乎仅创建次要分叉。干草叉分叉会导致移动点,因此我们推导出了这些分叉的临界性标准。我们的主要发现是,在该模型中出现了超临界漂移分叉,从而导致了稳定的行进点,而对于两分量版本而言,这似乎是不可能的。

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