Instabilities of horizontal magnetoconvection with rotating fluid in a sparsely packed porous media

We studied linear and nonlinear instabilities of horizontal magnetoconvection with rotating fluid in a sparsely packed porous media. We studied the critical Rayleigh number and traced marginal stability curves at different parameters , , , and . We obtained Takens‐Bogdanov and co‐dimension two bifurcation points. The Newell‐Whitehead multiple scheme was employed to derive amplitude equations at Pitchfork and Hopf bifurcation. At the onset of Pitchfork bifurcation we identified Eckhaus and Zigzag instability regions and studied Nusselt number. The system of coupled Landau Ginzburg equations were derived at the onset of Hopf bifurcation and identified secondary instability regions for fixed parameters, steady state mode shifted to standing and traveling waves as increases.