In this work, we study new system with a rich structure (the Shimizu-Morioka system), which is exhibiting the Lorenz-like dynamics.
Where the dot denotes the system obtained a Hopf bifurcation (Supercritical and subcritical) for some values of . For the analysis we use the center manifold and normal form theorem. A computer algebra system using Maple (version 9) was used to derive all the formulas and verifying the results presented in this work [Char, David].
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