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

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 evolu-tion 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