Analysis of a Five-Dimensional Chaotic Multistable Lorenz Model with a Sinusoidal Heating Function

For a long time, the Lorenz system has been a typical example for understanding the limits of nonlinear instability and predictability in atmospheric dynamics. In this study, we propose and examine a five-dimensional generalized Lorenz model in which the traditional constant heating parameter is replaced by a sinusoidal heating function, thereby accounting for periodically fluctuating thermal input. The additional dynamic variables describe secondary convective modes linked to multilayer heat transport. This means that there are more possible behaviors than in the classical three-dimensional model. We analyze the system’s symmetry, dissipativity, equilibrium structure, and local stability, and explore its intricate dynamics using one- and two-parameter bifurcation diagrams, Lyapunov exponents, and the Kaplan–Yorke dimension. The results show multiple attractors, multistability, and transitions between equilibrium, periodic, and chaotic regimes driven by crises. These results demonstrate that periodic thermal forcing can alter attractor geometry and trigger abrupt qualitative changes in system behavior, thereby affecting atmospheric regime shifts and constraints on predictability. The research emphasizes the influence of dimensionality and time-dependent heating on the configuration of chaotic convection models.