Nonreciprocity induces resonances in two-field Cahn-Hilliard model

Frohoff-Hülsmann, Tobias; Thiele, Uwe; Pismen, Len M.

Abstract

We consider a nonreciprocally coupled two-field Cahn-Hilliard system that has been shown to allow for oscillatory behavior 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 discuss possible interactions of linear modes and analyze the specific case of a ``Hopf-Turing'' resonance by discussing amplitude equations resulting from a weakly nonlinear approach.  The results obtained thereby 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.