Common Features of the Onset of the Persistent Chaos in Nonlinear Oscillators: A Phenomenological Approach

Bifurcational precedences of generating the persistent,crossing-the-potential-barrier chaos in nonautonomous, dissipative nonlinearoscillators are examined. The comparative computational study covers thetwin-well oscillator, pendulum with parametric excitation, and pendulumdriven by external harmonic force. The study reveals common features of thesystem response properties and of the bifurcational scenarios, prior to theonset of the chaos. It is pointed out that, in the three considered systems,the chaos is preceded by the two and only two asymmetric periodicattractors, which are simultaneously annihilated via theperiod-doubling-crisis scenario. However, the generating of the chaos is notnecessarily related directly to the escape from a potential well. We alsoshow that, in all three systems, the persistent chaos can be viewed as anirregular combination of the `crossing the potential barrier' and theoscillatory component of motion.

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