Hopf Bifurcation and Chaos in a Magnetoconvective Lorenz Model

This study explores how the Prandtl number affects the Hopf bifurcation point, which marks the loss of stability of steady convection, as well as the emergence of chaos, within the framework of a five-dimensional extended Lorenz model representing two-dimensional Rayleigh–Bénard magnetoconvection. We examine how variations in the magnetic field strength influence the stability of convective roll solutions and the occurrence of periodic and chaotic dynamics across a wide range of Prandtl numbers. This is carried out through a numerical computation of the Hopf bifurcation point (Hopf–Rayleigh number) from the eigenvalue spectrum of the Jacobian matrix at a nontrivial equilibrium point, while the dynamics are analyzed through Largest Lyapunov Exponent (LLE) plots obtained via numerical integration of the model equations using the classical Fourth-order Runge–Kutta (RK4) scheme. The onset of chaos is identified as the threshold at which chaotic behavior, characterized by a positive value of the LLE, emerges. The results demonstrate that variation of the Prandtl number significantly alters the stability and dynamics of the system at different magnetic field strengths. The observed multistability, the delayed transition to chaos and enhanced magnetic stabilization at high Prandtl numbers could potentially offer guidance for designing more reliable and efficient thermal management systems involving magnetohydrodynamic flows.