Diagnosis of periodic and chaotic responses in vibratory systems

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Abstract
This paper is devoted to the development of a new approach to distinguish between a chaotic and a periodic motion of a dynamical system. A criterion namely periodicity ratio is introduced to distinguish a periodic motion from a nonperiodic motion and differentiate chaos from a regular motion by a numerical procedure without plotting any figures. A Duffing’s equation and a nonlinear driven pendulum are analyzed by the periodicity ratio. Periodic–chaotic region diagrams are presented which allow a simultaneous comparison of periodic and chaotic behavior of a system with varying system parameters and a variety of initial conditions.

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