Amplitude death criteria for coupled complex Ginzburg-Landau systems

• DOI: 10.48550/arxiv.1803.02147
• Publication Date: 2018-01-01
• Authors: Robert A. Van Gorder; Andrew L. Krause; James A. Kwiecinski
• Keywords: Quintic function; Complex system

Amplitude death, which occurs in a system when one or more macroscopic wavefunctions collapse to zero, has been observed mutually coupled solid-state lasers, analog circuits, and thermoacoustic oscillators, name few applications. While studies have considered amplitude death on oscillator systems externally forced complex Ginzburg-Landau systems, route not studied autonomous continuum systems. We derive simple analytic conditions for the onset of wavefunction two equations with general nonlinear self- cross-interaction terms. Our results give theoretical underpinning recent reported literature, suggest an approach tuning parameters such so that they either permit prohibit (depending application). Numerical simulation equations, examples including cubic, cubic-quintic, saturable nonlinearities, is used illustrate analytical results.