Sequence of routes to chaos in a Lorenz-type system (Q779079)

A new chaotic system, which is a modification of the well-known Lorenz model, is proposed. A comprehensive study of the considered system is carried out, including the study of symmetry, equilibria, stability, and nonlinear dynamics. It is shown that, depending on the parity of the number \(n\), the system can exhibit different bifurcation behavior. Moreover, in the studied Lorenz-type system, many chaotic attractors are born from limit cycles with high periods in comparison with most known chaotic systems. It is also shown that, despite the unstability of all equilibria, only self-excited attractors are observed in the experiments, which distinguishes the proposed system from the known Lorenz model with hidden attractors. The results obtained help to better study the nature and variety of the occurrence of chaos in dynamical systems.