Rheostatic effect of a magnetic field on the onset of chaotic and periodic motions in a five-dimensional magnetoconvective Lorenz system
subject: Chaos; Hopf bifurcation; Lorenz; RayleighBard; Weakly nonlinear
description: This paper deals with a weakly nonlinear study of two-dimensional RayleighBard magnetoconvection using a simplified five-dimensional Lorenz model. The governing equations of the system are nondimensionalized and formulated in terms of the stream function and the scalar magnetic potential. A five-modal Fourier truncation scheme is employed and the resulting equations are scaled to obtain a five-dimensional autonomous dynamical system. The Hopf-Rayleigh number, signifying Hopf bifurcation, is numerically evaluated from the analysis of weakly nonlinear stability. Chaotic and periodic motions are depicted by plotting bifurcation diagrams, largest Lyapunov exponent (LLE) diagrams and three-dimensional projections of the phase-space. For a fixed set of parameter values, increasing the strength of the applied magnetic field is found to increase the Hopf-Rayleigh number, thereby delaying the destabilization of the system's equilibrium points. It is shown that while low magnetic field strengths favor the onset of chaotic motion directly from the steady state, stronger magnetic field strengths favor the onset of periodic convection from the steady state prior to the appearance of chaotic motion. We observe here that the applied magnetic field regulates the onset of chaotic and periodic motions in the system and therefore, has a rheostatic control over chaotic and periodic behaviors. 2025 Elsevier Ltd
creator: Siddheshwar, Pradeep G.; Suresh, Anoop; Kumar, M.S. Jagadeesh
source: Chaos, Solitons and Fractals;Volume;192;Issue;;Article No.;116020;
publisher: Elsevier Ltd
date: 01-01-2025
rights: Restricted Access; Hardcopy may be available in the library
relation: ISSN: 9600779; CODEN: CSFOE
format: online
language: English
type: Article
coverage: Siddheshwar P.G., Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bengaluru, 560029, India; Suresh A., Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Tamil Nadu, Vellore, 632014, India; Kumar M.S.J., Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Tamil Nadu, Vellore, 632014, India