On the dynamics of five- and six-dimensional Lorenz models

In this paperwe report on generalized Lorenzmodels. Fiveand six-dimensional Lorenzmodels are investigated, which are obtained by considering respectively two and three additional Fouriermodes in addition to themodes included in the derivation of the classical three-dimensional Lorenzmodel. Parameter planes, bifurcation diagrams, and attractors in the phase-space are used, in order to investigate the influence of the additional Fouriermodes on solutions, when comparedwith the solutions for the classical Lorenzmodel. It is shown that for parametersσ and b kept fixed, a larger parameter r results for the onset of chaos infive-and six-dimensional Lorenzmodels. Also it is shown that the shape of bifurcation diagrams, periodic, and chaotic attractors is preserved in both generalized Lorenzmodels. Additionally, it is shown that hyperchaos is observed only in the six-dimensional Lorenzmodel, at least in the parameter ranges here investigated.

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