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Low-Dimensional Description of Pulses under the Action of Global Feedback Control

Y. KanevskyA. A. Nepomnyashchy — 2012

Mathematical Modelling of Natural Phenomena

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...

Linear Stability of Fractional Reaction - Diffusion Systems

Y. NecA. A. Nepomnyashchy — 2010

Mathematical Modelling of Natural Phenomena

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...

Long-Wave Coupled Marangoni - Rayleigh Instability in a Binary Liquid Layer in the Presence of the Soret Effect

A. PodolnyA. A. NepomnyashchyA. Oron — 2008

Mathematical Modelling of Natural Phenomena

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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