Haim Lev, Hagberg Aric, Meron Ehud
Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.
Center for Nonlinear Studies, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Chaos. 2015 Jun;25(6):064307. doi: 10.1063/1.4921768.
We study resonant spatially periodic solutions of the Lengyel-Epstein model modified to describe the chlorine dioxide-iodine-malonic acid reaction under spatially periodic illumination. Using multiple-scale analysis and numerical simulations, we obtain the stability ranges of 2:1 resonant solutions, i.e., solutions with wavenumbers that are exactly half of the forcing wavenumber. We show that the width of resonant wavenumber response is a non-monotonic function of the forcing strength, and diminishes to zero at sufficiently strong forcing. We further show that strong forcing may result in a π/2 phase shift of the resonant solutions, and argue that the nonequilibrium Ising-Bloch front bifurcation can be reversed. We attribute these behaviors to an inherent property of forcing by periodic illumination, namely, the increase of the mean spatial illumination as the forcing amplitude is increased.
我们研究了经修改以描述在空间周期性光照下二氧化氯 - 碘 - 丙二酸反应的Lengyel - Epstein模型的共振空间周期解。通过多尺度分析和数值模拟，我们得到了2:1共振解的稳定性范围，即波数恰好是强迫波数一半的解。我们表明，共振波数响应的宽度是强迫强度的非单调函数，并且在足够强的强迫下减小到零。我们进一步表明，强强迫可能导致共振解的π/2相移，并认为非平衡伊辛 - 布洛赫前沿分岔可以被逆转。我们将这些行为归因于周期性光照强迫的一个固有特性，即随着强迫幅度增加平均空间光照也增加。
