Many physical, chemical or sometimes financial phenomena are considered as being only chaotic, or purely stochastic. However a deeper understanding of the inherent nature of these processes sometimes exhibits both deterministic and stochastic features. The original idea of the paper is to find new models taking into account both behaviors, stochastic and chaotic, in order to understand and predict better the real physical phenomena, but also to model data for different applications such as biomedical or financial processes. The hypothesis about the approximation of the real data by fractional Brownian motion has been validated based on statistics, and the estimation of the Hurst exponent successfully characterized the agressiveness of the chaotic component.