Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation

Frohoff-Hülsmann T; Thiele U

Abstract

Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatiotemporal pattern formation. Starting from a linear large-scale oscillatory instability—a conserved-Hopf instability—that naturally occurs in many active systems with two conservation laws, we derive a corresponding amplitude equation. It belongs to a hierarchy of such universal equations for the eight types of instabilities in homogeneous isotropic systems resulting from the combination of three features: large-scale vs small-scale instability, stationary vs oscillatory instability, and instability without and with conservation law(s). The derived universal equation generalizes a phenomenological model of considerable recent interest, namely, the nonreciprocal Cahn-Hilliard model, and may be of a similar relevance for the classification of pattern forming systems as the complex Ginzburg-Landau equation.