Author(s)

Jessé Rebello de Souza Junior, Claudio Gomes Fernandes

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

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.

Perron-Frobenius, Duffing Oscillator

Junior, J. and Fernandes, C. (2015) Probabilistic Approach in the Investigation of the Dynamics of a Duffing Oscillator. Applied Mathematics, 6, 1282-1293. doi: 10.4236/am.2015.68122.