We perform a bifurcation analysis of a two-dimensional magnetic Rayleigh–Bénard problem using a numerical
technique called deflated continuation. Our aim is to study the influence of the magnetic field on the bifurcation
diagram as the Chandrasekhar number 𝑄 increases and compare it to the standard (non-magnetic) Rayleigh–
Bénard problem. We compute steady states at a high Chandrasekhar number of 𝑄 = 103 over a range of the
Rayleigh number 0 ≤ Ra ≤ 105
. These solutions are obtained by combining deflation with a continuation of
steady states at low Chandrasekhar number, which allows us to explore the influence of the strength of the
magnetic field as 𝑄 increases from low coupling, where the magnetic effect is almost negligible, to strong
coupling at 𝑄 = 103
. We discover a large profusion of states with rich dynamics and observe a complex
bifurcation structure with several pitchfork, Hopf, and saddle–node bifurcations. Our numerical simulations
show that the onset of bifurcations in the problem is delayed when 𝑄 increases, while solutions with fluid
velocity patterns aligning with the background vertical magnetic field are privileged. Additionally, we report
a branch of states that stabilizes at high magnetic coupling, suggesting that one may take advantage of the
magnetic field to discriminate solutions.