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\begin{document}

\title{On Dynamics of Double-Diffusive Magnetoconvection in a Non-Newtonian
Fluid Layer}



\author[1]{Zhigang Pan}%
\author[2]{Yanlong Fan}%
\author[3]{Li Liang}%
\author[2]{Quan Wang}%
\affil[1]{Southwest Jiaotong University}%
\affil[2]{Sichuan University}%
\affil[3]{Sichuan University - Wangjiang Campus}%


\vspace{-1em}



  
  \date{May 14, 2024}


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\begin{abstract}
This article concerns the dynamic transitions of a non-Newtonian
horizontal fluid layer with thermal and solute diffusion and in the
presence of vertical magnetic field. First, a linear stability analysis
is done by deriving the principle of exchange of stability condition,
which shows the system loses stability when thermal Rayleigh number
exceeds a critical threshold. Second, we considered the transition
induced by real eigenvalues and complex eigenvalues, respectively, and
two nonlinear transition theorems along with several transition numbers
determining the transition types are obtained via the method of center
manifold reduction. Finally, rigorous numerical computations are
performed to offer examples of possible transitions, as well as the
stable convection patterns. Our results show that when the diffusivities
from big to small are thermal, solute concentration and magnetic
diffusion, both continuous and jump transitions can occur for certain
parameters; and if the diffusivities from big to small is the inverse of
the previous case, only continuous transition induced by real
eigenvalues are observed, which indicate a stationary convection.%
\end{abstract}%



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