The influence of a global delayed feedback control which acts on a system governed by a
subcritical complex Ginzburg-Landau equation is considered. The method based on a
variational principle is applied for the derivation of low-dimensional evolution models.
In the framework of those models, one-pulse and two-pulse solutions are found, and their
linear stability analysis is carried out. The application of the finite-dimensional model
allows to reveal...

Theoretical framework for linear stability of an anomalous sub-diffusive
activator-inhibitor system is set. Generalized Turing instability conditions are found to depend on
anomaly exponents of various species. In addition to monotonous instability, known from
normal diffusion, in an anomalous system oscillatory modes emerge. For equal anomaly
exponents for both species the type of unstable modes is determined by the ratio of the reactants'
diffusion coefficients. When the ratio exceeds its normal...

We have explored the combined long-wave Marangoni and Rayleigh instability of
the quiescent state of a binary- liquid layer heated from below or from above in the presence
of the Soret effect. We found that in the case of small Biot numbers there are two long-
wave regions of interest ~
and ~
. The dependence of both monotonic and
oscillatory thresholds of instability in these regions on both the Soret and dynamic Bond
numbers has been investigated. The complete...

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