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has been cited by the following article:

• TITLE: Probabilistic Approach in the Investigation of the Dynamics of a Duffing Oscillator

  AUTHORS: Jessé Rebello de Souza Junior, Claudio Gomes Fernandes

  KEYWORDS: Perron-Frobenius, Duffing Oscillator

  JOURNAL NAME: Applied Mathematics, Vol.6 No.8, July 24, 2015

  ABSTRACT: We develop in this text a probabilistic approach to deterministic nonlinear systems. By studying the spectral properties of the Frobenius-Perron operator of a Duffing oscillator, relevant dynamic properties of the system are identified. Using the characteristics of the Dirac operator, the evolution of the probability density function is obtained for the Duffing oscillator, allowing important aspects of this system to be investigated analytically. A comparison with numerical simulation is carried out in order to validate the results obtained by the analytical approach as well as to verify the nonsymmetric features of the oscillator response.