耦合复Ginzburg-Landau系统的振幅死亡准则
Amplitude death criteria for coupled complex Ginzburg-Landau systems
摘要：
在相互耦合的固体激光器、模拟电路和热声振荡器等应用中，已经观察到当一个或多个宏观波函数坍缩到零时在系统中发生的振幅死亡。虽然研究已经考虑了振荡器系统和外部强迫的复杂金-朗道系统的振幅死亡，但在自治连续统系统中尚未研究振幅死亡的途径。我们推导出一个宏观波函数的振幅死亡的发病简单的分析条件，在两个耦合的复杂的Ginzburg-Landau方程与一般的非线性自我和交叉相互作用条款。我们的研究结果给出了一个更一般的理论支撑最近的振幅死亡的结果在文献中报道，并建议在这样的系统中调整参数的方法，使他们要么允许或禁止振幅死亡的波函数（取决于应用）。数值模拟的耦合复杂的金-朗道方程，包括三次，五次，和饱和非线性的例子，被用来说明分析结果。
英文摘要：
Amplitude death, which occurs in a system when one or more macroscopic wavefunctions collapse to zero, has been observed in mutually coupled solid-state lasers, analog circuits, and thermoacoustic oscillators, to name a few applications. While studies have considered amplitude death on oscillator systems and in externally forced complex Ginzburg-Landau systems, a route to amplitude death has not been studied in autonomous continuum systems. We derive simple analytic conditions for the onset of amplitude death of one macroscopic wavefunction in a system of two coupled complex Ginzburg-Landau equations with general nonlinear self- and cross-interaction terms. Our results give a more general theoretical underpinning for recent amplitude death results reported in the literature, and suggest an approach for tuning parameters in such systems so that they either permit or prohibit amplitude death of a wavefunction (depending on the application). Numerical simulation of the coupled complex Ginzburg-Landau equations, for examples including cubic, cubic-quintic, and saturable nonlinearities, is used to illustrate the analytical results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
