We construct a seven-dimensional Lorenz model (7DLM) to discuss the impact of an extended nonlinear feedback loop on solutions' stability and illustrate the hierarchical scale dependence of chaotic solutions. The 7DLM requires a much larger critical value for the Rayleigh parameter (rc
∼ 116.9) for the onset of chaos. For chaotic solutions with r
= 120, high correlation coefficients among the modes at different scales indicate hierarchical scale dependence.