Search results for "inertial effects"
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Oscillatory periodic pattern dynamics in hyperbolic reaction-advection-diffusion models
2022
In this work we consider a quite general class of two-species hyperbolic reaction-advection-diffusion system with the main aim of elucidating the role played by inertial effects in the dynamics of oscillatory periodic patterns. To this aim, first, we use linear stability analysis techniques to deduce the conditions under which wave (or oscillatory Turing) instability takes place. Then, we apply multiple-scale weakly nonlinear analysis to determine the equation which rules the spatiotemporal evolution of pattern amplitude close to criticality. This investigation leads to a cubic complex Ginzburg-Landau (CCGL) equation which, owing to the functional dependence of the coefficients here involve…
Eckhaus instability of stationary patterns in hyperbolic reaction–diffusion models on large finite domains
2022
AbstractWe have theoretically investigated the phenomenon of Eckhaus instability of stationary patterns arising in hyperbolic reaction–diffusion models on large finite domains, in both supercritical and subcritical regime. Adopting multiple-scale weakly-nonlinear analysis, we have deduced the cubic and cubic–quintic real Ginzburg–Landau equations ruling the evolution of pattern amplitude close to criticality. Starting from these envelope equations, we have provided the explicit expressions of the most relevant dynamical features characterizing primary and secondary quantized branches of any order: stationary amplitude, existence and stability thresholds and linear growth rate. Particular em…