Abstract
In this paper, the theory of Lyapunov–Andronov is applied to investigate the route to chaos in Rossler system. On the base of a new analytical formula for the first Lyapunov value at the boundary of stability region, we make a detailed bifurcation analysis of this system. From the obtained results the following new conclusions are made: Transition to chaos in the Rossler's system takes place at soft stability loss in the form of a cascade of periodic self-oscillations. Then the occurrence of chaotic self-oscillations in this system takes place under hard stability loss.
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