Dynamics of Rössler Prototype-4 System: Analytical and Numerical Investigation

In this paper, the dynamics of a 3D autonomous dissipative nonlinear system ODEs-Rössler prototype-4 system, was investigated. Using Lyapunov-Andronov theory, we obtain new analytical formula for first Lyapunov’s (focal) value at boundary stability corresponding equilibrium state. On other hand, global analysis reveals that may exhibit phenomena Shilnikov chaos. Further, it is shown via calculations considered can be presented in form linear oscillator with one automatic regulator. Finally, found some combinations parameters, demonstrates chaotic behavior and transition from chaos to regular realized through inverse period-doubling bifurcations.