Broken Symmetry in Modified Lorenz Model

The Lorenz model is of interest because of its abundant bifurcations and dynamical phenomena, due largely to the presence of critical sets or non-definition sets. The model is investigated as a three-parameter quadratic family. This article further develops and refines a study of its basins of attraction, and it is explained by using two types of nonclassical singularity sets. This has an important impact on the number of preimages and shows the essential role played by the vanishing denominator in the inverses. A deeper analysis of the global dynamic properties of the model in the parameter ranges where three steady states exist, reveals the role of symmetry with an interesting and complex dynamic structure.