In this work, the dynamic behavior of a spin valve oscillator with a Nickel-free layer, modeled by the Landau-Lifshitz-Slonczewski equation is studied. It is considered a constant applied field and a spin current with two
components, a constant term and a term with a time-dependent harmonic modulation. Techniques to characterize dynamic behaviors of systems, such as Lyapunov exponents, bifurcation diagram, phase portraits, time
series, and Fourier spectra were used. It is demonstrated that the system presents multiple transitions between chaotic and regular states when the constant magnetic field, the magnitude, and frequency of the alternating current are varied. Furthermore, it is found that the effect of the magnetic field and the amplitude of the currents play a meaningful role in the chaotic behavior start.