Spatio-temporal secondary instabilities near the Turing-Hopf bifurcation
Por:
Ledesma-Duran, Aldo, Aragon, Jose L.
Publicada:
2 ago 2019
Categoría:
Multidisciplinary
Resumen:
In this work, we provide a framework to understand and quantify the
spatiotemporal structures near the codimension-two Turing-Hopf point,
resulting from secondary instabilities of Mixed Mode solutions of the
Turing-Hopf amplitude equations. These instabilities are responsible for
solutions such as (1) patterns which change their effective wavenumber
while they oscillate as well as (2) phase instability combined with a
spatial pattern. The quantification of these instabilities is based on
the solution of the fourth order polynomial for the dispersion relation,
which is solved using perturbation techniques. With the proposed
methodology, we were able to identify and numerically corroborate that
these two kinds of solutions are generalizations of the well known
Eckhaus and Benjamin-Feir-Newell instabilities, respectively. Numerical
simulations of the coupled system of real and complex Ginzburg-Landau
equations are presented in space-time maps, showing quantitative and
qualitative agreement with the predicted stability of the solutions. The
relation with spatiotemporal intermittency and chaos is also
illustrated.
Filiaciones:
Ledesma-Duran, Aldo:
Univ Nacl Autonoma Mexico, Ctr Fis Aplicada & Tecnol Avanzada, Blvd Juriquilla 3001, Queretaro 76230, Mexico
Aragon, Jose L.:
Univ Nacl Autonoma Mexico, Ctr Fis Aplicada & Tecnol Avanzada, Blvd Juriquilla 3001, Queretaro 76230, Mexico
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