Nonreciprocity induces resonances in two-field Cahn-Hilliard model

TL;DR

This paper investigates how non-reciprocal coupling in a two-field Cahn-Hilliard model leads to resonances, oscillatory states, and suppressed coarsening, using linear stability analysis, weakly nonlinear theory, and nonlinear simulations.

Contribution

It introduces a detailed analysis of resonance phenomena in a non-reciprocal two-field Cahn-Hilliard system, linking linear stability to nonlinear dynamics and simulations.

Findings

Resonances occur due to non-reciprocity in the model.

Linear instability thresholds match those of reaction-diffusion systems.

Weakly nonlinear analysis captures key nonlinear states.

Abstract

We consider a non-reciprocically coupled two-field Cahn-Hilliard system that has been shown to allow for oscillatory behaviour, a suppression of coarsening as well as the existence of localised states. Here, after introducing the model we first briefly review the linear stability of homogeneous states and show that all instability thresholds are identical to the ones for a corresponding Turing system (i.e., a two-species reaction-diffusion system). Next, we discuss possible interactions of linear modes and analyse the specific case of a ``Hopf-Turing'' resonance by discussing corresponding amplitude equations in a weakly nonlinear approach. The thereby obtained states are finally compared with fully nonlinear simulations for a specific conserved amended FitzHugh-Nagumo system. We conclude by a discussion of the limitations of the weakly nonlinear approach. The published version of this preprint can be found under T. Frohoff-Hu\"ulsmann, U. Thiele and L. M. Pismen. Nonreciprocity induces resonances in two-field Cahn-Hilliard model. Phil. Trans. R. Soc. A. 381: 20220087. 20220087. DOI: 10.1098/rsta.2022.0087