Probabilistic Approach in the Investigation of the Dynamics of a Duffing Oscillator

Jessé Rebello de Souza Junior, Claudio Gomes Fernandes

Naval Engineering Department, University of São Paulo, São Paulo, Brazil.

DOI: 10.4236/am.2015.68122                

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.

Keywords

Perron-Frobenius, Duffing Oscillator

Conflicts of Interest

The authors declare no conflicts of interest.

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