Linear/Quadratic Decomposition and Chaotic Features of the Lorenz Systems

This note talks about linear and quadratic decomposition remodeling and chaotic trajectories of the continuous-time Lorenz systems. More precisely, the Lorenz state-space differential equations are equivalently divided into linear and quadratic terms, based on which chaos dynamics are revisited by modifying or weighting the quadratic term and checking sign variation, respectively. The study shows that the quadratic term plays a key role in chaotic trajectories and behaviours of the Lorenz systems, which are summarized as a chaos conjecture, together with observation arguments and examples. Illustrations clearly reveal efficacy of the suggested linear/quadratic decomposition approach for chaos analysis.