Eckhaus instability of stationary patterns in hyperbolic reaction–diffusion models on large finite domains

Abstract We have theoretically investigated the phenomenon of Eckhaus instability stationary patterns arising in hyperbolic reaction–diffusion models on large finite domains, both supercritical and subcritical regime. Adopting multiple-scale weakly-nonlinear analysis, we deduced cubic cubic–quintic real Ginzburg–Landau equations ruling evolution pattern amplitude close to criticality. Starting from these envelope equations, provided explicit expressions most relevant dynamical features characterizing primary secondary quantized branches any order: amplitude, existence stability thresholds linear growth rate. Particular emphasis is given regime, where predict qualitatively different pictures. As an illustrative example, compared above-mentioned analytical predictions numerical simulations carried out modified Klausmeier model, a conceptual tool used describe generation vegetation stripes over flat arid environments. Our analysis has also allowed elucidate role played by inertia during transient unstable patterned state evolves towards more favorable stable configuration through sequences phase-slips. In particular, inspected functional dependence time location at which wavelength adjustment takes place as well possibility control quantities, independently each other.