Frohoff-Hülsmann Tobias, Thiele Uwe, Pismen Len M
Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, Münster 48149, Germany.
Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, Münster 48149, Germany.
Philos Trans A Math Phys Eng Sci. 2023 Apr 17;381(2245):20220087. doi: 10.1098/rsta.2022.0087. Epub 2023 Feb 27.
We consider a non-reciprocally coupled two-field Cahn-Hilliard system that has been shown to allow for oscillatory behaviour and suppression of coarsening. After introducing the model, we first review the linear stability of steady uniform states and show that all instability thresholds are identical to the ones for a corresponding two-species reaction-diffusion system. Next, we consider a specific interaction of linear modes-a 'Hopf-Turing' resonance-and derive the corresponding amplitude equations using a weakly nonlinear approach. We discuss the weakly nonlinear results and finally compare them with fully nonlinear simulations for a specific conserved amended FitzHugh-Nagumo system. We conclude with a discussion of the limitations of the employed weakly nonlinear approach. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.
我们考虑一个非互易耦合的双场Cahn-Hilliard系统，该系统已被证明会出现振荡行为并抑制粗化。在引入该模型后，我们首先回顾稳态均匀态的线性稳定性，并表明所有不稳定性阈值都与相应的双物种反应扩散系统的阈值相同。接下来，我们考虑线性模式的一种特定相互作用——“霍普夫-图灵”共振，并使用弱非线性方法推导相应的振幅方程。我们讨论弱非线性结果，最后将其与特定守恒修正FitzHugh-Nagumo系统的全非线性模拟结果进行比较。我们以对所采用的弱非线性方法局限性的讨论作为结论。本文是主题为“扩展系统图案形成和非线性动力学的新趋势”的一部分。
