Effects of boundary-temperature modulation on Rayleigh–Bénard convection: dynamics across convective and post-convective regimes

This study investigates the influence of time-periodic boundary-temperature modulation on the stability of a convective system. Linear stability analysis is employed utilizing perturbation analysis, Floquet theory and Hill’s infinite determinant method. Weakly non-linear stability analysis, through numerical solution of the resulting Lorenz system using Runge–Kutta method, characterizes chaotic and hyperchaotic behaviour via bifurcation diagrams and Lyapunov spectra. Results show that modulation amplitude and frequency significantly affect the route to chaos, with increasing amplitude generally having a destabilizing effect, and increasing frequency, stabilizing. Additionally, the presence of multiple positive Lyapunov exponents indicates hyperchaotic regimes, whose occurrence is shown to depend sensitively on modulation parameters. This work is the first of its kind to provide a comprehensive exploration of how boundary-temperature modulation can precipitate the onset of hyperchaotic behaviour, specifically showing its emergence within a three-dimensional, non-autonomous system.